  We describe "quasi canonical modules" for modular invariant rings $R$ of
finite group actions on factorial Gorenstein domains. From this we derive a
general "quasi Gorenstein criterion" in terms of certain 1-cocycles. This
generalizes a recent result of A. Braun for linear group actions on polynomial
rings, which itself generalizes a classical result of Watanabe for non-modular
invariant rings.
  We use an explicit classification of all reflexive rank one $R$-modules,
which is given in terms of the class group of $R$, or in terms of
$R$-semi-invariants. This result is implicitly contained in a paper of Nakajima
(\cite{Nakajima:rel_inv}).
