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. Because of its unusual properties with respect to charge conjugation and parity, it belongs to a nonstandard Wigner class. Consequently, the theory exhibits nonlocality 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.