Discrete Symmetries as Automorphisms of the Proper Poincaré Group

We present a consistent approach to finding discrete transformations in representation spaces of the proper Poincaré group. To this end we establish a correspondence between involutory automorphisms of the group and the discrete transformations. Such a correspondence allows us to describe the action of discrete transformations on arbitrary spin-tensor fields without any use of relativistic wave equations. Extending the proper Poincaré group by the discrete transformations, we construct explicitly fields carrying corresponding irreps.