  Freyd's generating hypothesis for the stable module category of a non-trivial
finite group G is the statement that a map between finitely generated
kG-modules that belongs to the thick subcategory generated by k factors through
a projective if the induced map on Tate cohomology is trivial. In this paper we
show that Freyd's generating hypothesis fails for kG when the Sylow p-subgroup
of G has order at least 4 using almost split sequences. By combining this with
our earlier work, we obtain a complete answer to Freyd's generating hypothesis
for the stable module category of a finite group. We also derive some
consequences of the generating hypothesis.
