Quillen Grassmannians as non-modular homotopy fixed points

The aim of this paper is to compute the homotopy fixed points of the homotopy action described by unstable Adams operations on the classifying spaces of unitary groups. The same technique can be applied to compute homotopy fixed points of the action of certain automorphisms on p-compact groups called generalized Grassmannians. We use the description of Quillen Grassmannians to describe the set of homotopy representations of elementary abelian p-groups into them.