So much for the speculation that Google might buy or pay off TiVo to resolve its DVR patent infringement case against Motorola Mobility’s home division — and facilitate a sale of the powerful set-top box operation. The search giant said this evening that it sold the business for $2.05B in cash and $300M in stock to Arris Group, a communications technology company. The news sent Arris shares up 16.9% in after hours trading. The company’s already on a roll, with its stock up 42% over the last 12 months. The deal “adds expertise in video and a larger presence in the home to our core strengths in voice and data, ensuring we are even better positioned to capitalize on and manage the evolution toward multi-screen home entertainment,” Arris CEO Bob Stanzione says. The companies report that Motorola’s home business generated $3.4B in revenues for the four quarters that ended in September, and that the deal should result in as much as $125M a year in cost savings. Google indemnified Arris against material risks from TiVo’s suit. That suggests “TiVo’s leverage tied to the sale was less than we thought,” says Lazard Capital Markets’ Barton Crockett. Google picked up the set-top box business last year when it paid $12.5B for Motorola Mobility, a major licensee of Android handset phones.