\title{Gluing representations via idempotent modules
\\ and constructing endotrivial modules}
\author{Paul Balmer}
\address{Department of Mathematics, ETH Z\"urich, 8092 Z\"urich, 
Switzerland}
\author{David J. Benson}
\address{Department of Mathematics, University of Aberdeen,
Aberdeen AB24 3UE, Scotland}
\author{Jon F. Carlson}
\address{Department of Mathematics, University of Georgia, 
Athens GA 30602, USA}

\begin{abstract}
Let $G$ be a finite group and $k$ be a field of characteristic $p$.
We show how to glue Rickard idempotent modules for a pair of
open subsets of the cohomology variety along an automorphism
for their intersection. The result is an endotrivial module.
An interesting aspect of the
construction is that we end up constructing finite dimensional
endotrivial modules using infinite dimensional Rickard idempotent
modules. We prove that a slight modification of
this construction produces a subgroup of finite index
in the group of endotrivial modules.
More generally, we also show how to glue any pair of $kG$-modules.
\end{abstract}