Homology of Steinberg algebras

Source abstract

Abstract We study homological invariants of the Steinberg algebra of an ample groupoid over a commutative ring . For any ample Hausdorff groupoid , we find that is a direct summand of ; using this and the Dennis trace we obtain a map . We study this map when is the (twisted) Exel–Pardo groupoid associated to a self‐similar action of a group on a graph, and compute and in terms of the homology of , and the ‐theory of in terms of that of .