New in Tiki21, you can manage calendar invitations, powered by SabreDAV, and using Tiki Webmail (powered by Cypht Webmail). See also CalDAV. This development was done as part of Email as a first-class citizen.
Use Tiki Webmail, and if Tiki webmail detects an invitation, it will offer you to add to a calendar (can be personal calendar or shared calendar)