2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/76065An important ingredient in the completion theorem of equivariant K-theory given by S. Jackowski is that the representation ring R(Gamma) of a compact Lie group satisfies two restriction properties called (N) and (R\_{F}). We give in this note sufficient conditions on a (compact) -space Z such that these properties hold with K\_{Gamma}^{*}(Z) instead of R(Gamma). As an example, we consider the space Z(Gamma;G) of the so called "elementary cocycles with coefficients in G" invented by H. Ibisch in his construction of a universal (Gamma;G)-bundle.Algebraic TopologyK-Theory and HomologyMSC2000: 19L47, 55N91text