  Let M^3 be a compact, oriented, irreducible, and boundary incompressible
3-manifold. Assume that its fundamental group is without rank two abelian
subgroups and its boundary is non-empty. We will show that every homomorphism
from pi_1(M) to PSL(2,C) which is not `boundary elementary' is induced by a
possibly branched complex projective structure on the boundary of a hyperbolic
manifold homeomorphic to M.
