Yes, you can sublet a rent-stabilized apartment in California—that is, unless your lease specifically prohibits subletting. If you are subletting your entire apartment, you may be prohibited from charging more than the amount you pay to your landlord. If you're just subletting a room in your apartment, then the amount you charge probably can't be more than that room's share of the total rent.
Certain jurisdictions, like Berkeley and San Francisco, limit how much you can charge your subletter if your unit is rent-stabilized.
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