I am currently holding a F visa with a 12 month expiration (US nationality). I work for a US firm with a China representative office. The company would like me to be there temporarily for 5-6 months to do business development. I will remain an employee of the US HQ office. Could I rent an apartment in Beijing with a F visa? If I need to register with the local police, would there be any problem?

Since each stay can't be longer than 30 days, I plan to fly out every month for 7 to 10 days.

Your advice will be highly appreciated. Thanks!