# The functor of complex characters of finite groups

## TL;DR

This paper analyzes the structure of a fibered biset functor related to complex class functions of finite groups, extending previous work by considering different fiber groups and revealing composition factors of p-permutation modules.

## Contribution

It completes the study of fibered biset functors by exploring various fiber groups, providing new insights into their structure and composition factors.

## Key findings

- Determined the structure of the fibered biset functor for complex class functions.
- Extended previous work to include different fiber groups.
- Identified composition factors of p-permutation modules.

## 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 $\mathbb C^\times$-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.