Just figured out how to display an author's K2 user group, thought I'd share in case it's helpful to anyone...

$this->item->author->profile->group is the group id number in the table k2_user_groups, an example:

<?php if($this->item->author->profile->group == 3): ?>
<?php echo "label for group 3"; ?>
<?php elseif($this->item->author->profile->group == 2): ?>
<?php echo "label for group 2"; ?>
<?php endif; ?>