Convex projective generalized Dehn filling

For d = 4,5,6, we exhibit the first examples of complete finite volume hyperbolic d-manifolds M with cusps such that infinitely many d-orbifolds M_m obtained from M by generalized Dehn filling admit properly convex real projective structures. The orbifold fundamental groups of M_m are Gromov-hyperbolic relative to a collection of subgroups virtually isomorphic to \mathbbZ^d-2, hence the images of the developing maps of the projective structures on M_m are new examples of divisible properly convex domains of the projective d-space which are not strictly convex, in contrast to the previous examples of Benoist.