The geometric Gamma-operation generation conjecture for equivariant bordism

Let $\Omega^{S^1}$ denote geometric $S^1$-equivariant bordism. For each irreducible representation $V$, let $\Gamma_V$ denote the corresponding operation in equivariant bordism, and suppose that geometric versions of these operations are defined. Linear actions on complex projective spaces provide geometric equivariant bordism classes.

Geometric Gamma-operation generation conjecture. $\Omega^{S^1}$ is generated over geometric versions of the operations $\Gamma_V$ by linear actions on projective spaces.

This conjecture would organize the geometric theory in parallel with the homotopical description of equivariant bordism. The source presents it as a framework for further investigation and gives no evidence that it is solved.