Mac mail outlook calendar invite

To follow up on this, I can now confirm that if I disable the calendar on the Exchange account and then click "Accept" for an invitation, it does NOT go to my mac calendar application in any way. I'll note that a search turned up other people with similar problems, so perhaps this is a bug that could be fixed?

Thanks for your response. I'm trying to reply by using the buttons that pop up at the top of the message within Mail:

These messages do not generate a notification in the calendar application.

I have not tried to do this from iCloud.com, as I would much prefer to be able to accept the invitation from within Mail.

Ah, I see. I actually don't have an iCloud email and I don't use that site. I'd prefer not to create yet another email address, and please let me know if there is some other way I can get you information that would be useful.

Now that I've added the outlook calendar, it does appear, and the invitations that I accepted appear in that calendar. Unfortunately I haven't received any new invitation so I can't check as to whether deselecting it changes anything, but I will note that when this all started, I did not have that calendar enabled, and the invitation did not go to any of my enabled calendars.

And as a follow-up, these events do seem to get added to an Outlook calendar (which I have not been using). Is there a way to direct mail to add these events to my mac calendar app instead?