OK, the problem comes from my Android version 4.1.2.
This is a feature request that calendars have an option to be merged on the smartphone.
Here is the use case:
Many people have an existing Google or Exchange calendar on their Android, the latter because you probably work in a company that has MS infrastructure (and you can’t change that). Your colleagues expect, that they see when you are busy or available. Either way it is difficult to let your spouse or husband, who is using Caldav with ownCloud or GroupOffice and where you would like to manage your calendar know your obligations.
I am not sure if DAVdroid could write and mirror into an existing calendar (ideally with an option, to mirror only events as “busy”) or if it would require a separate App, which would sync calendars locally on the smartphone. Any ideas / proposals are welcome, I am looking for a solution since many years, to combine calendars from proprietary and open source worlds.
This would be out of the scope of DAVdroid. DAVdroid is a sync adapter between Android and CalDAV/CardDAV, nothing more.
Did you already search the stores? In a quick search, I have found Copy Events which looks like what you need?