From The TimeSplitters Wiki

Invisibility is a large, yellow spheres with what appears to be some kind of cloak inside them. This power-up makes the user invisible for a short time. This is especially useful against human controlled opponents, but AI Bots tend to know where you are in TimeSplitters 2. In TimeSplitters: Future Perfect the cloak tends to work better against AI Bots, who won't usually discover the player using the cloak unless they are fired upon. The cloak doesn't offer complete invisibility against other players, however. The player will simply appear as a translucent outline of themselves, and they will still be visible on radar.

Trivia

• in TimeSplitters 2 if a player or AI bot that is a Scourge Splitter picks up a cloak, his purple flames are still visible.