Sergeant Cortez is the main protagonist of the TimeSplitters series, though he doesn't appear in the original TimeSplitters. As head of an elite unit of space marines, Cortez was one of the leading combatants in the TimeSplitter War, and the General's best soldier. He fought bravely alongside Corporal Hart.
Cortez appears coming from a worm-hole, with Reapers, Scourges and Berserkers following. He meets the heroes, and does not kill the Splitters, and allows them to live and help the heroes. They accept, and so they joined! This Cortez is the one from Future Perfect, and Anya still has connection with him.
Sometime later, the heroes find a Paralel-Universe Corporal Hart. She gets happy to see that Cortez is there, and introduces herself and joins the heroes.