  Resonances and final state interactions (FSI) play a role in the formation of
CP violation (CPV) constrained by CPT invariance. We provide a general
formulation of CPV including resonances and FSI starting from the CPT
constraint. Our discussion is elaborated within a simple $B$ decay model with
the $\rho$ and $f_0(980)$ resonances plus a non resonant background including
the $\pi\pi \to KK$ coupled amplitude. We consider few illustrative examples to
show the interference patterns appearing in the CP asymmetry, namely, that from
the $\rho$ resonance plus a non-resonant amplitude, and that from the
interference of the $\rho$ and $f_0(980)$ resonances. We perform the fit of the
CP asymmetry for the charmless three-body $B^\pm$ decay channel $B^{\pm}\to
\pi^{\pm} \pi^+\pi^-$ and obtain as outcome the $B^{\pm}\to \pi^{\pm} K^+K^-$
for $\pi\pi$ channel asymmetry in the mass region below $1.6$ GeV in fair
agreement with the new data LHCb data. Analogously, we also describe the CP
asymmetry of the $B^\pm\to K^\pm\pi^+\pi^-$ decay, with that from the $B^\pm\to
K^\pm K^+K^-$ channel obtained as output. As in the previous case, we also
found agreement with LHCb experimental data.
