Dark matter: A spin one half fermion field with mass dimension one?

We report an unexpected theoretical discovery of a spin one half matter field with mass dimension one. It is based on a complete set of eigenspinors of the charge conjugation operator. Due to its unusual properties with respect to charge conjugation and parity it belongs to a non standard Wigner class. Consequently, the theory exhibits non-locality with (CPT)^2 = - I. Its dominant interaction with known forms of matter is via Higgs, and with gravity. This aspect leads us to contemplate it as a first-principle candidate for dark matter.