Geodesic
The Covering Homotopy Extension Problem for Compact Transformation Groups
Matematičeskie zametki, Tome 92 (2012) no. 6, pp. 803-818

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It is shown that the orbit space of universal (in the sense of Palais) $G$-spaces classifies $G$-spaces. Theorems on the extension of covering homotopy for $G$-spaces and on a homotopy representation of the isovariant category $\operatorname{ISOV}$ are proved.
Keywords: $G$-space, covering homotopy, universal $G$-space in the sense of Palais, absolute (neighborhood) extensor, classifying space.
Mots-clés : compact transformation group, orbit space 
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     author = {S. M. Ageev and D. D. Repov\v{s}},
     title = {The {Covering} {Homotopy} {Extension} {Problem} for {Compact} {Transformation} {Groups}},
     journal = {Matemati\v{c}eskie zametki},
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     url = {http://geodesic.mathdoc.fr/item/MZM_2012_92_6_a0/}
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S. M. Ageev; D. D. Repovš. The Covering Homotopy Extension Problem for Compact Transformation Groups. Matematičeskie zametki, Tome 92 (2012) no. 6, pp. 803-818. http://geodesic.mathdoc.fr/item/MZM_2012_92_6_a0/