In Assassin's Creed IV: Black Flag, Great Inagua is the main headquarters of Edward Kenway's pirate crew.
Great Inagua is an island in the Caribbean that Edward acquires and develops as his base during the game. It contains the Great Inagua hideout, where the player can access upgrades and manage aspects of Edward's pirate operation. The location becomes a stable home for the crew as Edward moves between major ports and open-sea activities.
Nassau is also central to Black Flag and serves as a pirate settlement, but it is not Edward's personal headquarters. Havana and Kingston are major cities and trading ports, while Tortuga is another famous Caribbean pirate location that is not the answer. Black Flag combines fictionalized versions of real places with invented gameplay spaces. Great Inagua itself is a real island in the Bahamas, and the game uses its name for Edward's private base within the larger Caribbean map.