We show that the boundary of a projectively compact Einstein manifold of dimension n can be extended by a line bundle naturally constructed from the projective compactification. This extended boundary is such that its automorphisms can be identified with asymptotic symmetries of the compactification. The construction is motivated by the investigation of a new curved orbit decomposition for a n + 1 dimensional manifold which we prove results in a line bundle over projectively compact order one Einstein manifolds. This article is part of a discussion meeting issue ‘At the interface of asymptotics, conformal methods and analysis in general relativity’.