From cubical structures to the string orientation

Witten constructed a modular form-valued genus for any manifold with a $U<6>$-structure. Motivated by this,  Ando, Hopkins and Strickland characterized all ring maps from $MU<6>$ to even-periodic spectra in terms of cubical structures and characterized the Witten genus in these terms. 
In this talk, I will explore how one can combine their insights with equivariant topological modular forms to try to construct an equivariant string orientation, further refining the Witten genus.