The Green correspondence for infinitely generated modules
D. J. Benson and Wayne W. Wheeler
Submitted to Journal of the L.M.S., 1998.

\begin{abstract}
If $G$ is a finite group, then the usual version of the Green correspondence
applies to finitely generated $kG$-modules when $k$ is a field of
characteristic $p>0$ or a $p$-adic ring.  This paper presents a categorical
version of the Green correspondence and a version of the Burry--Carlson--Puig
Theorem that remain valid for arbitrary modules and coefficient rings.
In this generality, however, it is not clear whether the Green correspondent
of a finitely generated module is always finitely generated.
\end{abstract}