We consider the Burns-Flach formulation of the equivariant Tamagawa number conjecture (ETNC). In their setup, a Tamagawa number is an element of a relative K-group. We show that this relative group agrees with an ordinary K-group, namely of the category of locally compact topological modules over the order. Its virtual objects are an equivariant Haar measure in a precise sense. We expect that all relative K-groups in the ETNC will have analogous interpretations. At present, we need to restrict to regular orders, e.g. hereditary.

The author was supported by DFG GK1821 "Cohomological Methods in Geometry" and a Junior Fellowship at the Freiburg Institute for Advanced Studies (FRIAS)