On G-CW-complexes and the equivariant Whitehead theorem for compact Lie groups :
Takao Matumoto, On -CW complexes and a theorem of JHC Whitehead, J. Fac. Sci. Univ. Tokyo Sect. IA 18 (1971) 363-374 [irdb:00926/0001786419, PDF]
Takao Matumoto, Equivariant K-theory and Fredholm operators, J. Fac. Sci. Tokyo 18 (1971/72), 109-112 (pdf, pdf)
On detection of weak homotopy equivalences and equivariant weak homotopy equivalences in terms of free homotopy sets:
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