You can share task folders when you use exchange server mailboxes - right click on the folder, choose Properties and assign permissions to the group (preferred) or to each person.
If the group is in the Active Directory, for a distribution list for example, then you can use that to assign permission - all members of the group will get the same permission. They will also need "Folder visible" permission on the mailbox. See
sharing the folder - as long as it's a default folder, it can be opened using File, Open > Other users folder.