Question

Let Fk(G) be the k-space of class functions on G, given the inner product
[μ, ν] = 1/|G| *(Sum over g) μ(g^−1)ν(g).
Assuming that char k = 0, show that f = χM for some kG-module M iff [f,χi] is a nonnegative integer for all i.