Von Neumann invariants of coherent analytic sheaves (Q1579109)

Let \(Y\to X\) be a Galois covering of complex analytic spaces with Galois group \(G\) and \(X\) compact. Here the author constructs a theory of \(L^p\)-cohomology for coherent sheaves on \(Y\) equipped with a \(G\)-action. He can even handle the case in which the discrete group \(G\) acts on \(Y\) with fixed points (discrete co-compact action of \(G\) on \(Y)\) and the very important case in which on the sheaves acts a central extension of \(G\) by \(S^1\), obtaining a theory which contains the ``Vafa-Witten twisting trick'' introduced by Gromov. He obtains an Atiyah \(L^2\)-index theorem in this set-up.