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-ANEʹs) 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.