Compact group actions on equivariant absolute neighborhood retracts and their orbit spaces (Q617720)

The author gives another proof of his older result: If \(G\) is a compact Hausdorff group, \(H\) a closed normal subgroup and \(X\) a \(G\)-ANR space, then \(X/H\) is a \(G/H\)-ANR space (similarly for AR instead of ANR). The procedure uses the fact that every metrizable \(G\)-space embeds nicely into some \(C(G,L)\) (\(L\) a normed linear space) that is a rich \(G\)-space, \(G\)-AE and can be nicely approximated by a \(G\)-join.