Unfortunately, unless the aftermarket turbo charge which the engine has been modified with is CARB (California Air Resources Board) certified, the vehicle can not pass the smog check unless the component is removed and the original emissions configuration is restored.
We recommend following the link below to look up whether the turbo charger is legal for California use and installation on your Porsche Cayman.
https://ww3.arb.ca.gov/msprog/aftermkt/devices/amquery.php