  Let A be a finite dimensional algebra over a field of characteristic zero
graded by a finite abelian group G. Here we study a growth function related to
the graded polynomial identities satisfied by A by computing the exponential
rate of growth of the sequence of graded codimensions of A. We prove that the
G-exponent of A exists and is an integer related in an explicit way to the
dimension of a suitable semisimple subalgebra of A.
