  In this paper we prove a general structure theorem for relatively hyperbolic
groups (with arbitrary peripheral subgroups) acting naive convex co-compactly
on properly convex domains in real projective space. We also establish a
characterization of such groups in terms of the existence of an invariant
collection of closed unbounded convex subsets with good isolation properties.
This is a real projective analogue of results of Hindawi-Hruska-Kleiner for
${\rm CAT}(0)$ spaces. We also obtain an equivariant homeomorphism between the
Bowditch boundary of the group and a quotient of the ideal boundary.
