groupMembers.Cast<object>().ToList();
But that doesn’t look a good thing to do. You are creating a new empty list that will not be related to the original anymore.
The way you’re gonna be using these classes will tell if that would be a good idea.
If you’re planning to have both lists updated by adding items to a single class, it will not fit. Then maybe your DieGameAction should be generic as well: DieGameAction<T>.
Then you could give the original list without casting.
But, there’s another danger: if you set a new list to the IGroup, it will not be reflected to DieGameAction.
So, it all depends on what you’re trying to do.