Group Scheduling software

["AragonX" <aragonx dcsnow com>]

I'm looking for good group scheduling software.  Does anyone know of an
open source alternative to Microsoft Exchange?

Here is a list of features I'm looking for:

Shared calendars
Allows others to see your public calendar events
Allows user to enter private calender events
Syncs with the Palm (other PDAs would be nice)
Ability to assign To-Do tasks to other users
Can invite others to an event and keeps track of who has accepted and who
has a scheduling conflict

That's about it.  Any ideas?

Thanks in advance.