Rational magnetic equivariant K-theory

We introduce the magnetic equivariant K-theory groups as the K-theory groups associated to the magnetic groups and their respective magnetic equivariant complex bundles. We restrict the magnetic group to its subgroup of elements that act complex linearly, and we show that this restriction induces a rational isomorphism with the conjugation invariant part of the complex equivariant K-theory of the restricted group. This isomorphism allows us to calculate the torsion free part of the magnetic equivariant K-theory groups reducing it to known calculations in complex equivariant K-theory.