Re: Registered Agent
A business incorporated (or chartered or whatever the Canadian term is) in British Columbia (or anywhere else, for that matter) cannot conduct business on a regular basis in California unless it registers, pays the California franchise tax, and apponts an agent for the service of process.
Exceptions exist. Examples are isolated single transactions such as purchasing real estate, acting as a guarantor, etc.
Whether conducting business on the Internet triggers an obligation to register and appoint is a fast-developing area of the law, where the rules are still being formulated. Generally, merely webcasting ads that might be answered by Californians probably does not require registration. On the other hand, conducting a live, in-person auction would probably not only require registration and appointment of an agent, it would require complying with California laws regulating and licensing auctioneers.
I hasten to add that I have a lot of experience with auctions, and I think the registration, etc. requirements are sometimes lawfully circumvented by hiring a local licensed auctioneer to conduct the sale.
If you are inquiring because you have a prospective lawsuit and are wondering whom to serve, remember that you also have a jurisdiction issue. You may be able to get jurisdiction in California and serve the company at its BC headquarters even if it has no registered agent here, but jurisdiction issues are decided somewhat differently than obligation-to-register issues.