Equivariant Scott–Wojciechowski determinant formula

Let $H$ be a group, let $h\in H$, and let $D_P$ and $D_{\mathcal P_M}$ be the operators associated with the boundary conditions $P$ and ${\mathcal P}_M$. Let $A$ be the relevant boundary operator, let $K$ be the projection defining $P$, and let $a$ and $T$ be the operators appearing in the determinant-class expression. Write $\operatorname{Gr}_h^\infty(A)$ for the space of $h$-invariant smoothing projections associated with $A$. Equivariant Scott–Wojciechowski formula. For $h\in H$, the following equality holds over $\operatorname{Gr}_h^\infty(A)$:

$$\operatorname{det}^h_\zeta(D_P)=\operatorname{det}^h_\zeta(D_{\mathcal P_M})\cdot\operatorname{det}_F\left(\frac{a(\operatorname{Id}+T^{-1}K)}{2}\right).$$

This is presented as an equivariant version of the Scott–Wojciechowski theorem, relating the equivariant zeta-determinant of a boundary-value problem to a reference determinant and a Fredholm determinant. The supplied text does not state whether the formula has been proved or remains open.