In the sixties, Douglas proved that an isometric copy of an L¹-space inside of a second L¹-space is always contractively complemented. In the eighties, Kirchberg generalized this result to von Neumann algebras, showing that an isometric copy of the predual of a von Neumann algebra inside the predual of a second von Neumann algebra is always contractively complemented. We will show that the more natural setting for studying these questions is JBW^*-triples, a generalization of von Neumann algebras. These algebraic systems are of independent interest as exactly those dual Banach spaces whose unit ball has a transitive biholomorphic automorphism group. In this talk we will completely solve the contractive projection problem for preduals of such spaces.