How does phone access the airwaves using a GPS?

It connects to your phone via Bluetooth. All connectivity is done through the phone.

then the cell phone only uses the GPS as a repeater, so to speak, and is little different from a Bluetooth set in your ear. The actual physical phone still does all the work.

Correct

It simply connects two devices. It has a max range on the order of 20-50 feet (I think). In your case, the car and the GPS are functioning like a speaker and a microphone for your phone. That's all. Neither the GPS nor the car are communicating to the cell network or satellites for this function.

Did you mean "how does a GPS connect to cellular radio network?". It doesn't. The GPS communicates with your phone over bluetooth. That's all.

I believe that antenna (shaped like a shark fin) is satellite radio antenna and has nothing to do with bluetooth (or cellular network). Your car doesn't make phone calls either. Your phone does the work of calling/receiving calls and passes it on to your car audio system.

What function?

What function?

I did not clarify that, but I mean hands free. The car system understands me better than the GPS. But then the GPS does not have the best speech recognition anyway.

For what it's worth I'll stick to using the car system, especially since some controls are on the steering wheel.

Thanks for the explanation, I had actually thought the shark fin works the phone.

That's a good enough reason to use car audio system. It's so easy to engage the phone with a press of a button without taking our hands off the steering wheel and eyes off the road. Unfortunately mine locks up too much to be usable. It's great when it works but (3 out of 5 times) my phone restarts and the audio system freezes when I use it for phone calls.

The GPS receives the global positioning data from the satellites like an AM or FM radio receives a signal from a radio station transmitter. The GPS is a receiving only radio.

Then there is Bluetooth. BT is a two-way radio communication. The 2797 has a BT radio for communicating with the cell phone.

A cell phone, particularly a smartphone, can have numerous radios. There is the cell telephone radio, the GPS radio, the wi-fi radio, and the Bluetooth radio.

And, Near Field Communication (NFC)... think Apple Pay, Android, or Samsung Pay.

To add to Diesel's explanation, a cell phone will also use signals from nearby towers for location information. The Geo location of the tower is embedded in the handshaking the cell phone does with a tower when it connects to handle calls.

We had Equinox's as fleet vehicles a few years ago and that was a common problem. The phone would lock up or the audio. You couldn't end the call. The only way the dealer found to get out of the issue was to pull a battery terminal. We experimented and found if we activated "onstar" even though it wasn't active, the call would be released and we were good to go. Onstar over rides everything.