An equivariant Quillen theorem (Q1621452)

A well-known theorem of Quillen establishes an isomorphism \(\lambda: L \to MU_*\) where \(L\) is the Lazard ring (universal one-dimensional formal group law) and \(MU_*:= \pi_*(MU)\) is the coefficient ring of the unitary bordism ring. It is a reasonable goal to construct an equivariant generalization of Quillen's theorem. For compact abelian Lie groups \(A\) the notion of \(A\)-equivariant formal group laws was introduced in [\textit{M. Cole} et al., Proc. Lond. Math. Soc. (3) 81, No. 2, 355--386 (2000; Zbl 1030.55004)] and the homomorphism \(\lambda^A: L^A\to MU_*^A\) was constructed. However, it is an open question whether \(\lambda^A\) is an isomorphism. The main theorem of the paper claims that \(\lambda^{\mathbb Z/2}\) is an isomorphism.