The loop-space TMF to twisted K-theory map conjecture

Let $tmf$ denote topological modular forms, let $\Omega tmf$ denote its based loop object, and let $S^1$ act on $\Omega tmf\times S^1$; write $k/*$ for the target appearing in the proposed relation between loop-space $tmf$ and K-theory.

Loop-space TMF to twisted K-theory conjecture. There is a map

$$\left(\Omega tmf \times S^1\right)/S^1 \to k/*.$$

The proposed map is intended to express schematically how, for an eleven-dimensional circle-bundle description of M-theory, possibly equivariant twisted $tmf$ on $X^{10}\times S^1$ could give rise to twisted K-theory on $X^{10}$. Its existence and precise interpretation are not established in the source, so it remains open.