  We study the reduced Lefschetz module of the complex of p-radical and
p-centric subgroups. We assume that the underlying group G has parabolic
characteristic p and the centralizer of a certain noncentral p-element has a
component with central quotient H a finite group of Lie type in characteristic
p. A non-projective indecomposable summand of the associated Lefschetz module
lies in a non-principal block of G and it is a Green correspondent of an
inflated, extended Steinberg module for a Lie subgroup of H. The vertex of this
summand is the defect group of the block in which it lies.
