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We show that, besides the usual short distance contribution for CP violation,final state interactions together with CPT invariance can play an importantrole in the recent observation of CP violation in three-body charmless $B^\pm$decays. A significant part of the observed CP asymmetry distribution in theDalitz plot is located in a region where hadronic channels are stronglycoupled. We illustrate our discussion comparing the recent observation of CPviolation 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.

CP violation and CPT invariance in B+- decays with final state interactions