CPT violation implies violation of Lorentz invariance.
A interacting theory that violates CPT invariance necessarily violates Lorentz invariance. On the other hand, CPT invariance is not sufficient for out-of-cone Lorentz invariance. Theories that violate CPT by having different particle and antiparticle masses must be nonlocal.
Greenberg
O W
OW
Center for Theoretical Physics, Department of Physics, University of Maryland, College Park, Maryland 20742-4111, USA. owgreen@physics.umd.edu