ICS invites are added to calendar, but no acceptance sent
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)
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