| Résume | This is joint work with Paul Balmer and Dave Benson. Suppose that $G$ is a finite group and k is a field of characteristic $p > 0$. The endotrivial $kG$-modules are the elements of the Picard group of invertible objects in the stable category of $kG$-modules. They form an important subgroup of the group of all self equivalences of the stable category. In addition, endotrivial modules play a significant role in the block theory and modular representation theory of $G$. In this paper we investigate a new construction of endotrivial modules, which is not limited to $p$-groups. The method is a gluing construction developed by Balmer and Favi applied to the idempotent modules of Jeremy Rickard. |
