  If a finite group acts holomorphically on a pair (X,L), where X is a complex
projective manifold and L a line bundle on it, for every k the space of
holomorphic global section of the k-th power of L splits equivariantly
according to the irreducible representations of G. We consider the asymptotic
growth of these summands, under various positivity conditions on L. The methods
apply also to the context of almost complex quantization.
