I ran into confusion in the Warlock forum.  Whenever I try to deal with rules and mechanics I get things wrong, so I'm going to ask the people who are good at this stuff.

Can a Warlock with the Hexblade Patron, and The Pact Boon: Pact of the Blade, summon a Two-Handed weapon, and use the Great Weapon Master Feat with it?

Here is my problem:

Hex Warrior

At 1st level, you acquire the training necessary to effectively arm yourself for battle. You gain proficiency with medium armor, shields, and martial weapons.

The influence of your patron also allows you to mystically channel your will through a particular weapon. Whenever you finish a long rest, you can touch one weapon that you are proficient with and that lacks the two-handed property. When you attack with that weapon, you can use your Charisma modifier, instead of Strength or Dexterity, for the attack and damage rolls. This benefit lasts until you finish a long rest. If you later gain the Pact of the Blade feature, this benefit extends to every pact weapon you conjure with that feature, no matter the weapon’s type.

Pact of the Blade

You can use your action to create a pact weapon in your empty hand. You can choose the form that this melee weapon takes each time you create it (see the Weapons section for weapon options). You are proficient with it while you wield it. This weapon counts as magical for the purpose of overcoming resistance and immunity to nonmagical attacks and damage.

Your pact weapon disappears if it is more than 5 feet away from you for 1 minute or more. It also disappears if you use this feature again, if you dismiss the weapon (no action required), or if you die.

You can transform one magic weapon into your pact weapon by performing a special ritual while you hold the weapon. You perform the ritual over the course of 1 hour, which can be done during a short rest. You can then dismiss the weapon, shunting it into an extradimensional space, and it appears whenever you create your pact weapon thereafter. You can’t affect an artifact or a sentient weapon in this way. The weapon ceases being your pact weapon if you die, if you perform the 1-hour ritual on a different weapon, or if you use a 1-hour ritual to break your bond to it. The weapon appears at your feet if it is in the extradimensional space when the bond breaks.

Warlocks start out knowing how to use Simple weapons, then at 1st level, Hex Warrior gives them the ability to use Martial weapons, but it specifically states that they cannot have the Two-Handed Property.  Someone was talking about a Hexblade build, and said something about using the Great Weapon Master Feat.  I pointed out that Warlocks can't do that, and everyone who posted after that told me I was wrong.

Hex Warrior

At 1st level, you acquire the training necessary to effectively arm yourself for battle. You gain proficiency with medium armor, shields, and martial weapons.

The influence of your patron also allows you to mystically channel your will through a particular weapon. Whenever you finish a long rest, you can touch one weapon that you are proficient with and that lacks the two-handed property. When you attack with that weapon, you can use your Charisma modifier, instead of Strength or Dexterity, for the attack and damage rolls. This benefit lasts until you finish a long rest. If you later gain the Pact of the Blade feature, this benefit extends to every pact weapon you conjure with that feature, no matter the weapon’s type.

The answer is yes, you can turn a two-handed weapon (both melee and ranged) into your pact weapon with the Pact of the Blade feature, thus qualifying them for your Hex Warrior feature as well as your Great Weapon Master feat. The key is the last sentence of the Hex Warrior feature I marked in bold.

This Sage Advice by Jeremy Crawford supports this interpretation.

You can do it, but you need to use a physical weapon and declare it to be your pact weapon, is the way I understand it. You can’t create one out of thin air like you can with pact of the blade, you can just make a regular sword your pact weapon. 

Oops. I had something backwards in my head. see below.

yeah that makes since i had the same problem with carnage's great scythe

Quote from Xalthu >>

You can do it, but you need to use a physical weapon and declare it to be your pact weapon, is the way I understand it. You can’t create one out of thin air like you can with pact of the blade, you can just make a regular sword your pact weapon. 

 The wording specifically says "conjure" so I think it is meant to apply to both cases.

Quote from TexasDevin >>

Quote from Xalthu >>

You can do it, but you need to use a physical weapon and declare it to be your pact weapon, is the way I understand it. You can’t create one out of thin air like you can with pact of the blade, you can just make a regular sword your pact weapon. 

 The wording specifically says "conjure" so I think it is meant to apply to both cases.

Pact of the Blade

You can use your action to create a pact weapon in your empty hand. You can choose the form that this melee weapon takes each time you create it (see the Weapons section for weapon options).

The weapon definitely does not need to exist already. The wording in the Pact of the Blade feature makes it very clear that the weapon is created.

Basically, you can't use two-handed weapons with the Hex Warrior ability, unless it is your Pact of the Blade pact weapon.  It doesn't matter if the pact weapon is created from nothing or from a real magic weapon (Pact of the Blade says "create" with either option).  Also, Great Weapon Master doesn't specifically say it works with only two-handed weapons, but with "heavy" melee weapons (and then only the second bullet, the first has no restriction, and is intended to work with any melee weapon), so the second point would work in any case so long as the weapon in question had the "heavy" property, regardless of being two-handed.

So from level 1 to 3 (and onward, if you don't take Pact of the Blade), you can use Hex Warrior with a "real" weapon that isn't two-handed.  From level 3 on (with Pact of the Blade) you can use any melee weapon you conjure (create) with the pact with the Hex Warrior Ability.  The first bullet of GWM will work in any case, and the second with any "heavy" weapon, real or conjured from the pact.

Quote from iconarising >>

Basically, you can't use two-handed weapons with the Hex Warrior ability, unless it is your Pact of the Blade pact weapon.  It doesn't matter if the pact weapon is created from nothing or from a real magic weapon (Pact of the Blade says "create" with either option).  Also, Great Weapon Master doesn't specifically say it works with only two-handed weapons, but with "heavy" melee weapons (and then only the second bullet, the first has no restriction, and is intended to work with any melee weapon), so the second point would work in any case so long as the weapon in question had the "heavy" property, regardless of being two-handed.

So from level 1 to 3 (and onward, if you don't take Pact of the Blade), you can use Hex Warrior with a "real" weapon that isn't two-handed.  From level 3 on (with Pact of the Blade) you can use any melee weapon you conjure (create) with the pact with the Hex Warrior Ability.  The first bullet of GWM will work in any case, and the second with any "heavy" weapon, real or conjured from the pact.

 

 It is true that GWM specifies Heavy weapons, not Two-handed weapons. But to make things easier, all mundane weapons that are heavy are also two-handed. Not vice versa though.

Quote from BeyondMisty >>

Quote from iconarising >>

Basically, you can't use two-handed weapons with the Hex Warrior ability, unless it is your Pact of the Blade pact weapon.  It doesn't matter if the pact weapon is created from nothing or from a real magic weapon (Pact of the Blade says "create" with either option).  Also, Great Weapon Master doesn't specifically say it works with only two-handed weapons, but with "heavy" melee weapons (and then only the second bullet, the first has no restriction, and is intended to work with any melee weapon), so the second point would work in any case so long as the weapon in question had the "heavy" property, regardless of being two-handed.

So from level 1 to 3 (and onward, if you don't take Pact of the Blade), you can use Hex Warrior with a "real" weapon that isn't two-handed.  From level 3 on (with Pact of the Blade) you can use any melee weapon you conjure (create) with the pact with the Hex Warrior Ability.  The first bullet of GWM will work in any case, and the second with any "heavy" weapon, real or conjured from the pact.

 

 It is true that GWM specifies Heavy weapons, not Two-handed weapons. But to make things easier, all mundane weapons that are heavy are also two-handed. Not vice versa though.

 I was making the distinction in case someone homebrews a "heavy" weapon without the two handed property, but you are correct that the "standard" offerings with "heavy" are also two handed.

What others have said. Hex Warrior lets you use CHA for attacks with pact weapon regardless of the type.

Yes, you can turn a greatsword into your pact weapon with the Pact of the Blade feature as the benefit extends to every pact weapon you conjure with that feature, no matter the weapon’s type, which can include two-handed weapons. 

Ok.  Thanks everyone. All is clear now.