  Let G=GL(n,q), SL(n,q) or PGL(n,q) where q is a power of some prime number p,
let U denote a Sylow p-subgroup of G and let R be a commutative ring in which p
is invertible. Let D(U) denote the derived subgroup of U and let e be the
central primitive idempotent of the group algebra RD(U) corresponding to the
projection on the invariant RD(U)-submodule. The aim of this note is to prove
that the R-algebras RG and eRGe are Morita equivalent (through the natural
functor sending an RG-module M to the eRGe-module eM).
