On the relative K-group in the ETNC, Part III

The previous papers in this series were restricted to regular orders. In particular, we could not handle integral group rings, one of the most interesting cases of the ETNC. We resolve this issue. We obtain versions of our main results valid for arbitrary non-commutative Gorenstein orders. This encompasses the case of group rings. The only change we make is using a smaller subcategory inside all locally compact modules.