CPT violation implies violation of Lorentz invariance.

@article{Greenberg2002CPTVI,
  title={CPT violation implies violation of Lorentz invariance.},
  author={O. W. Greenberg},
  journal={Physical review letters},
  year={2002},
  volume={89 23},
  pages={
          231602
        }
}
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. 
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