Abstract
We determine the structure of the fibered biset functor sending a finite group G to the complex vector space of complex valued class functions of G. Previously, it is studied as a biset functor by Bouc and as a C×-fibered biset functor by Boltje and the second author. In this paper, we complete the study by considering proper non-trivial subgroups of C× as the fiber group. As a corollary, we obtain a (previously known) set of composition factors of the biset functor of p-permutation modules.
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