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In this paper we prove a general structure theorem for relatively hyperbolicgroups (with arbitrary peripheral subgroups) acting naive convex co-compactlyon properly convex domains in real projective space. We also establish acharacterization of such groups in terms of the existence of an invariantcollection 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 theBowditch boundary of the group and a quotient of the ideal boundary.

The structure of relatively hyperbolic groups in convex real projective geometry