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 $\mathbb C^\times$-fibered biset functor by Boltje and the second author. In this paper, we complete the study by considering the other choices of the fiber group. As a corollary, we obtain a (previously known) set of composition factors of the biset functor of $p$-permutation modules.

中文翻译：

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有限群复数函子

我们确定了将有限群 $G$ 发送到 $G$ 的复值类函数的复向量空间的纤维二集函子的结构。以前，它被 Bouc 研究为双集函子，Boltje 和第二作者将其作为 $\mathbb C^\times$ 纤维化的双集函子进行研究。在本文中，我们通过考虑纤维组的其他选择来完成研究。作为推论，我们获得了一组（先前已知的）$p$-permutation 模块的双集函子的组合因子。