Answer to Question #18637 in Abstract Algebra for Irvin

Question

Let e = (Sum over g∈G) a_g * g ∈ kG be an idempotent, where k is a field and G is a finite group. Let χ be the character of G afforded by the kG-module kG • e. Show that for any h ∈ G, χ(h) = |CG(h)| (Sum over g∈C)•a_g,
where C denotes the conjugacy class of h^−1 in G.