In Assassin's Creed, the Templar artifact that projects a map and can control minds is the Apple of Eden.
The Apple of Eden is one of the series' Pieces of Eden, technologically advanced artifacts created by the First Civilization. In the first game, the Templars seek it because its effects can influence perception and behavior. The artifact also produces a projected map that reveals locations associated with other Pieces of Eden.
The object is carried by Robert de Sablé's forces and later becomes central to Al Mualim's betrayal. Its powers help establish the series' recurring conflict: the Templars want to use such technology to impose order, while the Assassins oppose control over human freedom.
“Apple of Eden” is a specific artifact name, while “Pieces of Eden” is the broader category. Other games introduce additional Pieces, including staffs, swords, and shrouds, so those terms are related but not interchangeable answers.