A note on the higher Atiyah-Patodi-Singer index theorem on Galois   coverings
  Let $\Gamma$ be a finitely generated discrete group satisfying the rapid decay condition. We give a new proof of the higher Atiyah-Patodi-Singer theorem on a Galois $\Gamma$-coverings, thus providing an explicit formula for the higher index associated to a group cocycle $c\in Z^k (\Gamma;\mathbb{C})$ which is of polynomial growth with respect to a word-metric. Our new proof employs relative K-theory and relative cyclic cohomology in an essential way. 
Alexander Gorokhovsky, Hitoshi Moriyoshi, Paolo Piazza
math.DG math.KT