Affine torsor structure for faithful Galois extensions

Determine whether, for every faithful Galois extension of E-infinity rings A to B with finite group G, the morphism Spec B to the quotient stack Spec B/G is an affine G-torsor over some base stack M distinct from Spec B/G.

Background

The paper compares affine torsors arising from pi_0-Galois extensions with Rognes' broader notion of faithful G-Galois extensions of E-infinity rings. For a pi_0-Galois extension A to B, Spec B to Spec A is an affine G-torsor, but the converse relationship does not directly extend to arbitrary faithful Galois extensions.

The example KO to KU shows the issue: although this is a faithful C_2-Galois extension, the map Spec KU/C_2 to Spec KO is not an equivalence. The paper asks whether replacing Spec A by the quotient stack Spec B/G restores an affine torsor description over a suitable auxiliary base stack. A later proposition gives a positive answer for certain Landweber-exact, complex-periodic, bounded-height E-infinity rings, but the general question remains unresolved.