  Let G be a finite group. The stable module category of G has been applied
extensively in group representation theory. In particular, it has been used to
great effect that it is a triangulated category which is compactly generated.
  Let H be a subgroup of G. It is possible to define a stable module category
of G relative to H. It too is a triangulated category, but no non-trivial
examples have been known where this relative stable category was compactly
generated.
  We show here that the relative stable category is compactly generated if the
group algebra of H has finite representation type. In characteristic p, this is
equivalent to the Sylow p-subgroups of H being cyclic.
