  Let G be a topological group such that its homology H(G) with coefficients in
a principal ideal domain R is an exterior algebra, generated in odd degrees. We
show that the singular cochain functor carries the duality between G-spaces and
spaces over BG to the Koszul duality between modules up to homotopy over H(G)
and H^*(BG). This gives in particular a Cartan-type model for the equivariant
cohomology of a G-space. As another corollary, we obtain a multiplicative
quasi-isomorphism C^*(BG) -> H^*(BG).
  A key step in the proof is to show that a differential Hopf algebra is formal
in the category of A-infinity algebras provided that it is free over R and its
homology an exterior algebra.
