Linearization of proper group actions (Q1030203)

Let \(G\) be a locally compact group which acts properly, in the sense of Palais, on a space \(X\) that is metrizable by a \(G\)-invariant metric. The authors prove that \(X\) can be equivariantly embedded in a normed space \(E\) endowed with a linear isometric \(G\)-action which is proper on \(E\setminus\{0\}\). Moreover, there exists a normed space \(N\) and a closed \(G\)-embedding of \(X\) into \((E\setminus\{0\})\times N\). If in addition \(G\) is a Lie group, then \(E\setminus\{0\}\) and \((E\setminus\{0\})\times N\) are equivariant absolute extensors.