  Let $R$ be a commutative Noetherian ring and let $\G$ be the category of
modules of G-dimension zero over $R$. We denote the associated stable category
by $\pG$. We show that the functor category $\modpG$ is a Frobenius category
and we argue how this property could characterize $\G$ as a subcategory of
$\modR$.
