Let G be a compact connected Lie group and K a closed connected subgroup. Assume that the order of any torsion element in the integral cohomology of G and K is invertible in a given principal ideal domain R. It has been known since around 1970 that in this case the cohomology of the homogeneous space G/K with coefficients in R and the torsion product of H^*(BK) and R over H^*(BG) are isomorphic as R-modules. I am going to explain that this isomorphism is multiplicative and natural in the pair (G,K) provided that 2 is invertible in R. The essential new ingredient of the proof is the notion of a homotopy Gerstenhaber algebra, whose definition will be recalled.