The connective real $K$–theory of Brown–Gitler spectra

Abstract

We calculate the connective real $K$–theory homology of the mod $2$ Brown–Gitler spectra. We use this calculation and the theory of Dieudonné rings and Hopf rings to determine the mod $2$ homology of the spaces in the connective $\Omega$–spectrum for topological real $K$–theory.