Spinor representation of the general Lorentz group for spin 1/2   particles and CPT
  We show that the attempt to introduce all of the discrete space-time transformations into the spinor representation of the Lorentz group as wholly independent transformations (as in the vectorial representation) leads to an 8-component spinor representation in general. The first indications seem to imply that CPT can be violated in this formulation without going outside of field theory. However one needs further study to reach a final conclusion. 
Recai Erdem