Orbit nonproper actions on Lorentz manifolds

If a topological group G acts on a topological space X, then we say that the action is orbit nonproper provided that, for some x is an element of X, the orbit map g --> gx : G --> X is nonproper. We consider the problem of classifying the connected, simply connected real Lie groups G such that G admits a locally faithful, orbit nonproper action on a connected Lorentz manifold. In this paper, we describe three collections of groups such that G admits such an action iff G is in one of the three collections. In an earlier paper, we effectively described the first collection. In yet another paper, we describe effectively those groups in the second collection which are not contained in the union of the first and third. Finally, in another paper, we describe effectively the third collection.