(This is a very slightly modified version of a preprint previously
titled "A local description of the stable category")

Title:    Local subgroups and the stable category
Author:   Wayne W. Wheeler
Address:  Center for Communications Research, 4320 Westerra Court,
          San Diego, CA 92121
Date:     February 2002
Status:   To appear in Transactions of the AMS

Abstract:  If $G$ is a finite group and $k$ is an algebraically closed
field of characteristic $p>0$, then this paper uses the local subgroup
structure of $G$ to define a category $\mathfrak L(G,k)$ that is
equivalent to the stable category of all left $kG$-modules modulo
projectives.  A subcategory of $\mathfrak L(G,k)$ equivalent to the
stable category of finitely generated $kG$-modules is also identified.