  Our aim is to transfer several foundational results from the modular
representation theory of finite groups to the wider context of profinite
groups. We are thus interested in profinite modules over the completed group
algebra k[[G]] of a profinite group G, where k is a finite field of
characteristic p.
  We define the concept of relative projectivity for a profinite k[[G]]-module.
We prove a characterization of finitely generated relatively projective modules
analogous to the finite case with additions of interest to the profinite
theory. We introduce vertices and sources for indecomposable finitely generated
k[[G]]-modules and show that the expected conjugacy properties hold - for
sources this requires additional assumptions. Finally we prove a direct
analogue of Green's Indecomposability Theorem for finitely generated modules
over a virtually pro-p group.
