The presence of a complex structure and cellular (co)homology make it easy to see that the cohomology ring of "G"/"H" is concentrated in even degrees, but in fact, something much stronger can be said. Because "G" → "G/H" is a principal "H"-bundle, there exists a classifying map "G"/"H" → "BH" with target the classifying space "BH". If we replace "G"/"H" with the homotopy quotient "G""H" in the sequence "G" → "G/H" → "BH", we obtain a principal "G"-bundle called the Borel fibration of the right multiplication action of "H" on "G", and we can use the cohomological Serre spectral sequence of this bundle to understand the fiber-restriction homomorphism "H"*("G"/"H") → "H"*("G")