Due to the decreasing performance of Android on my Nexus 10 and similar reports of other user I tried to install CyanogenMod 13. This caused some resolvable problems...
The CyanogenMod wiki entry is great point to start. In the build selection i chose the latest snapshot build to get a recent CM13.
The default nano variant of Open Gapps delivered no working Play Store, therefore I had to select the micro variant. (More complete variants are to big for the system partition)
After my installation of the micro variant, the Google Play Services keept crashing with an exception:
java.lang.SecurityException: "gps" location provider requires ACCESS_COARSE_LOCATION or ACCESS_FINE_LOCATION permission.
To resolve this problem I made an factory reset and during the initial startup I had to answer more questions. Therefore I assume the initial setup with the nano variant did not provide valid settings for the later installed micro variant.
After installing the apps I used before on Android, the tablet is now really fast and usable again!