# Generic character sheaves on disconnected groups and character values

## TL;DR

This paper extends the theory of character sheaves to disconnected reductive groups, linking geometric objects with representation characters over finite fields, generalizing known results from connected groups.

## Contribution

It introduces a framework connecting generic character sheaves on disconnected groups with representation characters, broadening the scope of geometric representation theory.

## Key findings

- Established a correspondence between character sheaves and representation characters for disconnected groups.
- Extended known results from connected to disconnected reductive groups.
- Provided new tools for studying representations via geometric methods.

## Abstract

We relate a generic character sheaf on a disconnected reductive group with a character of a representation of the rational points of the group over a finite field extending a result known in the connected case.