It is legal to build your own firearm for personal use, as long as you can legally own a firearm. No serial number is required. However, it is suggested to engrave a serial number, model, and manufacturer on your receiver or frame in case it is lost or stolen. You must complete the lower or frame yourself - it is not legal for you to purchase and have another person finish it for you. All regulations under the National Firearms Act (NFA), issued by the Bureau of Alcohol, Tobacco, Firearms, and Explosives (ATF), and other related regulations apply to your firearm.
This is also true for the state of California.
Quoted from the ATF website:
"Individuals manufacturing sporting-type firearms for their own use need not hold Federal Firearms Licenses (FFLs). However, we suggest that the manufacturer at least identify the firearm with a serial number as a safeguard in the event that the firearm is lost or stolen. Also, the firearm should be identified as required in 27 CFR 478.92 if it is sold or otherwise lawfully transferred in the future."
Source: http://www.atf.gov/firearms/faq/firearms-technology.html
Please review the NFA before using any product distributed by Stealth Arms:
https://www.atf.gov/content/firearms/firearms-industry/national-firearms-act
Please review all ATF regulations before using any product distributed by Stealth Arms:
https://www.atf.gov/content/firearms
Additionally, you may create a short-barreled rifle out of your firearm via a BATFE (Bureau of Alcohol Tobacco Firearms and Explosive) Form 1 after BATFE approval.
*Stealth Arms does not provide guidance or legal opinions on whether or not its products should or should not be used or manufactured in your specific state, county, or city. It is the customer's sole responsibility to make that decision.