The status of this question is <i>OPEN</i>.

This theory has <i>NOT</i> been developed yet.

That being said, the evidence is as compelling as ever, I don't know of any obstructions to making this work, and I'm convinced that there's an awesome theory out there, waiting to be discovered.

Roughly 8 years ago, I wrote an unsuccessful ERC proposal, where I outlined a program. This proposal can be found on my Utrecht website [here][1] and [here][2] (warning: that website will probably stop existing one year from now, so the links will become broken -- but the linked material will still be there to be found on whatever new website I end up having in the future). 

There are small bits and pieces of what one might call progress, which I've made available on my website:

[Here's one][3]. In this draft, I take a compact simply connected Lie group $G$ of dimension $d$, and I consider the map $p:G\to \{pt\}$. I construct, geometrically, the $TMF$-pushforward $p_!(1)\in TMF^{-d}(\{pt\})=\pi_d(TMF)$ of the element $1\in TMF^0(G)$ along the map $G\to \{pt\}$.

[Here's another one][4]. In this draft, I show that there's a new type of 2-equivariance for $TMF$, where the group of equivariance gets replaced by a fusion category.


  [1]: https://web.archive.org/web/20161027180429/http://www.staff.science.uu.nl/~henri105/Grants/CNTMF-B1.pdf
  [2]: https://web.archive.org/web/20161027180429/http://www.staff.science.uu.nl/~henri105/Grants/CNTMF-B2.pdf
  [3]: https://web.archive.org/web/20170702204522/http://www.staff.science.uu.nl/~henri105/PDF/OW-report-STcocycles.pdf
  [4]: https://web.archive.org/web/20170702204744/http://www.staff.science.uu.nl/~henri105/PDF/EquivariantElliptic.pdf