(I've been wrong, and will be wrong again, it's no big deal. It does make for an interesting business situation. Google will own a cell company and set top box company. Within Motorola, the business groups are pretty separate, these divisions can be split just as easily as they were combined.)
They really never were combined. GI was always handled separately from the cell group. I don't even know what may be common among them except for common upper management. GI is and always has been in Horsham and the cellular group has been in Libertyville for many years. I worked for both. Patent law for GI and licensing for cellular.
GI never liked being part of Motorola and I don't doubt that they wouldn't mind being spun back out again.