  We show that, besides the usual short distance contribution for CP violation,
final state interactions together with CPT invariance can play an important
role in the recent observation of CP violation in three-body charmless $B^\pm$
decays. A significant part of the observed CP asymmetry distribution in the
Dalitz plot is located in a region where hadronic channels are strongly
coupled. We illustrate our discussion comparing the recent observation of CP
violation in the $B^\pm\to K^\pm K^+ K^-$ and $B^\pm\to K^\pm \pi^+ \pi^-$
phase space, with a calculation based on $\pi\pi\to KK$ scattering.
