Subalgebras of group cohomology defined by infinite loop spaces

We study natural subalgebras ChE(BG;R) of group cohomology H*(BG;R) defined in terms of the infinite loop spaces in spectra E and give representation theoretic descriptions of those based on QS0 and the Johnson-Wilson theories E(n). We describe the subalgebras arising from the Brown-Peterson spectra BP and as a result give a simple reproof of Yagita's theorem that the image of BP*(BG) in H*(BG;Fp) is F-isomorphic to the whole cohomology ring; the same result is shown to hold with BP replaced by any complex oriented theory E with a non-trivial map of ring spectra E→HFp. We also extend our constructions to define subalgebras of H*(X;R) for any space X; when X is a finite CW complex we show that the subalgebras ChE(n)(X;R) give a natural unstable chromatic filtration of H*(X;R).