When I play Akshan and steal a tapped gear, does it stay tapped or untapped?

When you use Akshan's ability to steal a piece of gear, the gear's status (tapped/exhausted or untapped/ready) does not change.

According to the core mechanics of Riftbound, when you gain control of a permanent, it retains its current state (exhausted or ready) unless a card effect specifically instructs you to change it. Because Akshan's ability only moves the gear to your base and changes its controller, the gear remains in the same tapped (exhausted) state it was in before it was stolen.

Note: This is my interpretation based on standard game mechanics regarding control-change and state. No official FAQ exists for this specific interaction regarding the state of stolen gear.