Ditto in checking if the GM has been coded to check for the presence of FBZV/DWA (remote central locking and anti-theft alarm siren).
Question: are you only "arming/disarming" DWA (anti-theft alarm siren system) using the remote buttons on the key? Or have you tried arming/disarming using the key manually in the driver's door lock cylinder?
Either way should arm/disarm the system. But if using the buttons on the keyfob...the arming/disarming signal is transmitted over an RF (radio frequency) that is either 315 MHz (in North America) or 433 MHz (in Europe and many other markets in Asia & Africa). And in this case, the key's RF signal must match the frequency of the receiver.
With the info in the above paragraph...another question arises...and that is...does the RF of the key match the RF of the receiver? BMW makes keys and receivers that are either 315 MHz or 433 MHz: