Wall groups of finite groups and $\Pi$-signatures of manifolds

This article contains the evaluation of the image of the natural homomorphism $\chi$ from the even-dimensional Wall group $L_{2k}(\Pi)$ into the ring of complex representations of a finite group $\Pi$. The computations are carried out for finite groups acting freely and linearly on spheres, by means of a differential-topological interpretation of $\chi$; the Atiyah–Singer invariant is utilized as a tool.
Bibliography: 8 titles.