Mozilla Lightning, a calendar extension for the Mozilla mail client Thunderbird, just released version 0.3. This version includes rudimentary support for Microsoft Exchange meeting invitations. It's still a very early release with a bit of a clunky UI, but the basic mechanisms, like add-to-calendar and alarms, are there.

One notable drawback: Lightning does not put accepted invitations on your Exchange calendar, only your local calendar. Putting meetings on your server-side calendar is essential to prevent people from scheduling conflicting meetings. So the early adopter best practice would have to be to accept the invite in Lightning first to set up the reminder on your Linux desktop, then accept it again in Outlook to make sure it's on your public calendar.