This is a continuation of [N-S 1, 2, 3], which wc refer to as I, II, and III. In this series of papers fake Lie groups and adic fake Lie groups are studied. We will recall some of the basic definitions. Further notations and terminology may be found in I, II, and lI1. An adic fake Lie group of type G, G a compact connected Lie group, is a finite loop space X, such that the classifying space is in the adic genus of BG, i.e BG and BX are equivalent after localisation at ~ or any p-completion. X is a fake Lie group of type G if X is in the genus of BG, i.e X and BG are p-local equivalent for every prime, genusoA(BG) denotes the adic genus and genus(BG) the genus of BG. A maximal torus for a (adic) fake Lie group X of type G is a map J r : BTx -~ BX, Tx a torus, such that the homotopy fiber o f f r has the homotopy type of a finite CW-complex, and such that rank(Tx) = rank(X) = rank(G). The Weyl group Wx is defined to be the set of homotopy classes of homotopy equivalences ,q : BTx -~ BTx, such that fT-'7,q _~.[7,. In I. 3.7, 3.6, it is proved that Wx ~ WG as abstract groups. One of the main goals was and is to determine all fake Lie groups allowing a maximal torus. In II and III, this is done for simply connected Lie groups and unitary groups. Here we will extend these results to the general case.