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Sorry to hear you’re facing problems 
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Nextcloud version (eg, 20.0.5): 27.1.3
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PHP version (eg, 7.4): 8.1.2
The issue you are facing:
I would like to have Nextcloud setup so that if I add an external user to a calendar event (ex. someone with a gmail account), it would properly sync and track on my Nextcloud calendar, when the user accepts the event, and any changes to it they would make on their end, including their response.
Currently I add them and it sends the request but if they accept the event, it shows they have not done anything on my instance in the Nextcloud calendar. Not sure if the issue would lie in Nextcloud or have a problem due to using a private dovecot email server in the communication piece.
So I’m really not certain where to target the problem.