Quote from ProfessorWhen »Assume a game with YOU and players A and B
So, what happens is:
1. YOU steal A's Grizzly Bears with Threaten and equip Assault Suit to it.
2. YOU end the turn and player A regains control of his Grizzly Bears which is still equipped.
3. At the beginning of Player A's upkeep Assault Suit triggers, then you can choose to have player A or B gain control of the creature.
4. Repeat this for player B during his turn.
5. At the end of the turn it goes back to player A. (The Suit's control change effect ends.)
5. At the beginning of your upkeep YOU can choose to give it to player A or B (it is currently controlled by player A.