The homotopy-orbit conjecture for the framed bordism bicategory

Let $SO(2)$ act on the symmetric monoidal bicategory $\mathbb{F}_{cfd}$ of framed two-dimensional bordisms with fully dualizable objects. Write $(\mathbb{F}_{cfd})_{SO(2)}$ for the bicategory of co-invariants, or homotopy orbits, of this action, and let $\operatorname{Cob}_{2,1,0}^{\mathrm{or}}$ denote the oriented bordism bicategory. The homotopy-orbit conjecture. The bicategory of co-invariants is monoidally equivalent to the oriented bordism bicategory:

$$(\mathbb{F}_{cfd})_{SO(2)}\cong\operatorname{Cob}_{2,1,0}^{\mathrm{or}}.$$

Moreover, the colimit defining the homotopy orbits is compatible with the monoidal structure. This equivalence would identify oriented bordisms as the homotopy orbits of framed bordisms and would provide the missing comparison needed to derive the Cobordism Hypothesis for oriented manifolds by passing from fixed points to homotopy orbits; the source presents it as a natural conjecture.