Quaternionic algebraic cycles and reality, by Pedro F. dos Santos and Paulo Lima-Filho

In this paper we compute the equivariant homotopy type of spaces of algebraic cycles on real Brauer-Severi varieties, under the action of the Galois group Gal(C/R). Appropriate stabilizations of these spaces yield two equivariant spectra. The first one classifies Dupont/Seymour's quaternionic K-theory, and the other one classifies and equivariant cohomology theory Z^*(-) which is a natural recipient of characteristic classes KH^*(X) --> Z^*(X) for quaternionic bundles over Real spaces X.

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