Geodesic
Wall groups of finite groups and $\Pi$-signatures of manifolds
Sbornik. Mathematics, Tome 27 (1975) no. 2, pp. 163-181

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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. 
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     author = {G. A. Kats},
     title = {Wall groups of finite groups and $\Pi$-signatures of manifolds},
     journal = {Sbornik. Mathematics},
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G. A. Kats. Wall groups of finite groups and $\Pi$-signatures of manifolds. Sbornik. Mathematics, Tome 27 (1975) no. 2, pp. 163-181. http://geodesic.mathdoc.fr/item/SM_1975_27_2_a1/