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Are you the original owner of the vehicle? When the vehicle starts and runs by itself. Does the dash and radio light up and work without putting in the key?
You might want to contact onstar. The previous owner might of had onstar do a remote start.
The other thing is maybe some close to where you are has a remote that your vehicle picked up and started the vehicle.
That would rule out another remote. I would contact Onstar ask them if a remote start was requested.
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Thank you again.