Legal Question in Business Law in California

The answer is, generally, yes. It may either be permitted or required depending upon exactly what you mean by "register." If you mean "form" a business entity such as a corporation or limited liability company under California laws, you'll need to appoint someone with a California address as your registered agent for service of process; attorneys do this as do agent or incorporation-services companies that make this part of their regular business. Also, if your business is formed elsewhere (such as Alberta or Nevada), it may register in California even if it does no business here, but wants, for example, to protect the availability of its name. Finally, a foreign (Alberta, Nevada, etc.) business that will be transacting business within California (as by hiring employees, soliciting sales, etc.) probably must obtain from the California Secretary of State a "certificate of qualification" by filing the prescribed form containing some basic information about the business and identifying its agent for the service of process within California. See California Corporations Code sections 2101-2106 (available on line).