Air compressor?

 

On my 09 GTS there is a connection under the front passenger seat for an air-hose. The air-hose is in the rear near the spare tire.

As long as the GTS has air-suspension (which I believe they all are??) then it's part of the vehicle.

 

yes, the car has an air compressor for the suspension. However, if you plan to use it for filling the tires, be prepared for a very long process. The suspension uses only a very small amount of air to work properly.
I have an 09 GTS, and I carry a small 12volt air compressor for the tires.