ICS invites are added to calendar, but no acceptance sent [duplicate]
Open the Contacts app, select your own email address in the list of contacts. In the menu on top of the screen, go to "Card" -> "Make this my card". Ensure your email address is entered as part of your card. Reload calendar. Then it should work, you will get a notification popup with accept/decline buttons. (I just had the same problem, on a Mac running Yosemite) Source