2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/61761A successful generalization of phantom map theory to the equivariant case for all compact Lie groups is obtained in this paper. One of the key observations is the discovery of the fact that homotopy fiber of equivariant completion splits as product of equivariant Eilenberg-Maclane spaces which seems impossible at first sight by the example of Triantafillou.Algebraic Topology55P91,55P60text