Straightening and bounded cohomology of hyperbolic groups

It was stated by M. Gromov [Gr2] that, for any hyperbolic group G, the map from bounded cohomology H-b(n)(G,R) to H-n(G,R) induced by inclusion is surjective for n greater than or equal to 2. We introduce a homological analogue of straightening simplices, which works for any hyperbolic group. This implies that the map H-b(n)(G, V) --> H-n(G, V) is surjective for n greater than or equal to 2 when V is any bounded QG-module and when V is any finitely generated abelian group.