There are some classical examples of Real equivariant cohomology theories and twisted cohomology theories, including equivariant KR-theory in Atiyah and Segal's paper, and the more general construction, Freed-Moore K-theory. Most of the examples are related to K-theory.
I'm curious whether there is a general definition of "twisted Real equivariant cohomology theory". Should it just be the joint of twisted, Real, and equivariant cohomology theories? Should there be any desired relations between the three aspects, the Realness, equivariance, and twists? Is there any reference? Thanks.
