Discussion of $\mathbb{Z}_2$-equivariant stable homotopy groups/equivariant stable cohomotopy of spheres:
On real oriented cohomology theory in general and in particular on Real cobordism cohomology and Real K-theory:
Shôrô Araki, $\tau$-Cohomology Theories, Japanese Journal of Mathematics 4 2 (1978) 363-416 [doi:10.4099/math1924.4.363]
Shôrô Araki, Forgetful spectral sequences, Osaka Journal of Mathematics 16 1 (1979) 173-199 [Euclid]
(the relevant spectral sequences)
Shôrô Araki, Orientations in $\tau$-cohomology theories, Japan Journal of Mathematics (N.S.) 5 2 (1979) 403-430 [doi:10.4099/math1924.5.403]
On generalization of the h-cobordism theorem to equivariant cobordism:
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