Shares of ARRIS Group, a high-speed Internet and cable TV equipment company, traded higher Thursday a day after the company announced it was acquiring the home business of Google’s Motorola Mobility subsidiary for $2.35 billion in cash and stock.

After Wednesday’s close at $14.54, the stock reached as high as $15.90 Thursday before retreating.

The deal will allow ARRIS, based in the Suwanee area, to become a bigger player in the delivery of video, but it also allows Google to get out of the cable set-top boxes business that is the core of Motorola Home and reduce Google’s potential exposure to patent disputes over cable technology.

ARRIS Chairman and CEO Bob Stanzione discussed the deal Wednesday in a conference call with analysts, saying it “represents a great leap forward for ARRIS.” According to Bloomberg, Stanzione said the deal will help Arris become more “relevant” in providing set-top boxes, allow it to get products to market faster and help the company provide equipment to customers whose cable sets do not support the delivery of video via the Internet.

Under the deal announced Wednesday, Google would gain a nearly 16 percent stake in ARRIS, the companies said. Google will receive $2.05 billion in cash and about $300 million in newly issued ARRIS shares.

In November, Jefferies & Co. analyst James Kisner reiterated a “buy”rating on Arris, speculating at the time that it could strike a deal with Motorola Home. Kisner also said in November that Apple Inc. might rely on ARRIS’ technology for its highly anticipated Apple TV. In a report obtained by Barrons.com, Kisner wrote:

“Our discussions with industry contacts suggest that at least one major N. American MSO is working to estimate how much additional capacity may be needed for a new Apple device on their broadband data network. We believe this potentially suggests an imminent launch of the Apple TV, a positive development for ARRIS, who is directly exposed to data traffic growth from incremental IP video streams on cable networks.” MSO refers to multiple system operators that own and operate cable TV systems.

The deal with ARRIS comes seven months after Google completed its $12.4 billion purchase of Motorola Mobility, which included the home set-top box business.

Motorola Home generated revenues of $3.4 billion for the four quarters ended Sept. 30, twice the revenue that ARRIS generated during the same period. The combined companies are expected to generate about $100 million to $125 million in annual cost savings, the companies said. ARRIS and Motorola Home will have more than 500 customers in 70 countries.

“This transformational combination of two complementary businesses will create a leading end-to-end provider of today’s video, data and voice products, and tomorrow’s next-generation IP-based broadband products,” Stanzione said in announcing the deal Wednesday.

Despite unloading Motorola Home, Google still would be responsible for most of any damages or settlements involving a patent lawsuit filed against Motorola Home by digital video recorder provider TiVo Inc., Arris said. TiVo is seeking billions of dollars in damages, claiming Motorola’s cable TV boxes infringe on its patents.

“Google has taken that risk off the table,” Stanzione said during the conference call.

It’s possible the deal could add to the size of ARRIS’ workforce in metro Atlanta, where the company has about 450 employees, spokesman Alex Swan said Wednesday. The company, which has its headquarters in Forsyth County, has 2,100 employees worldwide.

A year ago, Arris announced a deal to acquire BigBand Networks, a California-based supplier of digital video networking solutions to broadband service providers. Arris said the deal would extend the company’s capabilities in the processing, management and distribution of digital video content.

The deal with Motorola Home is expected to close before the end of June, assuming it gets regulatory approval.