Not sure whether this is an evolution bug or a libgdata bug.  Was testing in Karmic Koala and found this issue.  Was advised that this issue was upstream from Ubuntu so reporting it here.

Steps taken to reproduce issue:
1. Open Evolution
2. Set up a Google calendar in Evolution (Under calendar, select "new calendar" type of "Google" and enter credentials)
3. Receive a meeting invitation in Evolution.
4. In the invitation, select your Google calendar and hit "Accept"
5. Receive the error "Unable to send item to calendar '<Google calendar name>'. Authentication failed."

Expected behavior: To accept the meeting request and publish the event to the Google calendar

Actual behavior: Rejected due to "failed authentication."

I can create a Google calendar event from Evolution outside the context of accepting a meeting invite, so the authentication should work for accepting an invite as well.