Why we use τ^-1 in constructing an acceptor for Lτ

Let G_L be the transition relation of a generator for L and let A_L be the transition relation of an acceptor for L. Then A_L = G_L^-1. Clearly G_Loτ is the transition relation of a generator for Lτ. Therefore (G_Loτ)^-1 is the transition relation of an acceptor for Lτ. But (G_Loτ)^-1 = (τ)^-1oG_L^-1 = (τ)^-1oA_L.