  Let $M$ be a finite dimensional modular representation of a finite group $G$.
We consider the generating function for the non-projective part of the tensor
powers of $M$, and we write $\gamma_G(M)$ for the reciprocal of the radius of
convergence of this power series. We investigate the properties of the
invariant $\gamma_G(M)$, using tools from representation theory, and from the
theory of commutative Banach algebras.
