UPDATE 1-Continental buys fleet management tech provider Zonar

* Conti to buy 81 pct of Zonar; Daimler to keep 19 pct stake

* Zonar provides telematics systems for fleet operators

* Conti shares close up 0.8 percent (Adds details on companies to be acquired)

FRANKFURT, Oct 4 (Reuters) - German automotive group Continental has agreed to buy U.S. smart fleet management technology provider Zonar for an undisclosed price to expand its mobility services and strengthen its position in the United States, it said on Tuesday.

Continental said it would buy 81 percent of Seattle, Washington-based Zonar, while German car and truck maker Daimler would keep its 19 percent stake.

Zonar provides telematics systems that enable customers such as large truck fleet operators to roll out satellite-based connectivity services such as remote vehicle diagnostics. It has over 300 employees.

The move is growing evidence of a shift by carmakers and their suppliers from physical vehicles and parts to mobility services as customers increasingly rent cars instead of buying them, while services tend to command higher profit margins.

Shares in Continental rose on the news and closed 0.8 percent higher at 188.70 euros, broadly in line with the German blue-chip DAX.

“Through the integration of new smart technology solutions, we can enhance our existing fleet management services. In addition, with regard to remote diagnostics for commercial vehicles, we can broaden our existing Continental diagnostics capabilities,” said Michael Ruf, head of Continental’s Commercial Vehicle & Aftermarket unit, where the acquisition will be integrated.

Continental said it also bought Indiana-based Hoosier Racing Tire on Monday, declining to disclose a purchase price. (Reporting by Georgina Prodhan; Editing by Edward Taylor and David Evans)