We are interested in obtaining local nets in the sense of Haag--Kastler from unitary representations of a connected Lie group G. A natural sets of axioms naturally leads to a causal structure on M. We focus on the case where M = G/P is a flag manifold of a simple Lie group G, or a covering space thereof. Then G must be hermitian Lie group and M a conformal compactification of a Euclidean Jordan algebra V. It's simply connected covering is a simple space-time manifold in the sense of Mack--de Riese. We show that the unitary representations permitting non-trivial nets are the positive energy representations (direct integrals of lowest weight representatiosn). These nets have several interesting features. One is that the ``wedge regions'' that link the geometry of M to the modular theory of the algebras involved are given by the intervals (double cones) of W.~Bertram's cyclic order on M. Another is that locality properties of the net can be specified in terms of open G-orbits in the space of pairs, which is most interesting for covering spaces because the number of these orbits corresponds to the number of sheets in the covering. Note: This talk is part of the activity of the MUR Excellence Department Project MatMod@TOV (CUP E83C23000330006) The Operator Algebra Seminar schedule is here: https://sites.google.com/view/oastorvergata/home-page?authuser=0