If you set the Email for the Home calendar to 'None' (right-click the calendar in the left pane, Properties), then accepted invitations should be added automatically to the Google calendar.

http://forums.mozillazine.org/viewtopic.php?p=14789141#p14789141

thanks sfhowes when i change the home calendar to 'none' and try to accept an invite you'll see what happens in the picture attached. It says "no writable calendars are configured for invitations, please check the properties."

If you right-click the Google calendar in the left pane of the Calendar tab, Properties, is Read only checked, and is the gmail address in the Email field? Which add-on syncs the calendar?

I cannot find a read only check box. Could you post a picture showing where it is? My gmail account is listed under the "share with specific people" label but I feel this is not the correct place you are asking about. This is found under "settings" associated in the left pane of google calendar with my calendar. I am using Provider for Google Calendar as my add-on.

The attached picture shows the Properties window shown by right-clicking the Google calendar. Note that I added the calendar directly as a CalDAV network calendar, without using an add-on.

thanks the link and photo were very helpful!