Orbit spaces of proper equivariant absolute extensors

Let G be a locally compact Hausdorff group. We study orbit spaces of equivariant absolute neighborhood extensors (G-ANE's) in the category of all proper G-spaces that are metrizable by a G-invariant metric. We prove that if a proper G-space X is a G-ANE (respectively, a G-ANE(n),n⩾0), and H a closed normal subgroup of G such that all the H-orbits in X are metrizable, then the H-orbit space X/H is a G/H-ANE (respectively, a G/H-ANE(n)). Other related results are also established.