CP and discrete flavour symmetries

We give a consistent definition of generalised CP transformations in the context of discrete flavour symmetries. Non-trivial consistency conditions imply that every generalised CP transformation can be interpreted as a representation of an automorphism of the discrete group. This allows us to give consistent generalised CP transformations of popular flavour groups. We are able to clear up issues concerning recent claims about geometrical CP violation in models based on T′, clarify the origin of ”calculable phases” in Δ(27) and explain why apparently CP violating scalar potentials of A4 result in a CP conserving ground state.