Tilting-object conjecture for equivariant matrix factorizations of invertible polynomials

Let ${\bf w}\in {\mathbb C}[x_1,\ldots,x_n]$ be an invertible polynomial, let $\Gamma_{\bf w}$ be its group of diagonal symmetries, and let $\operatorname{mf}({\mathbb A}^n,{\bf w},\Gamma_{\bf w})$ be the corresponding category of equivariant matrix factorizations. Tilting-object conjecture. For any invertible polynomial ${\bf w}$, the category

$$\operatorname{mf}({\mathbb A}^n,{\bf w},\Gamma_{\bf w})$$

has a tilting object. This is stated for $n=3$ in earlier work, while the general assertion is presented here as a conjecture and is related by Orlov's theorem to the tilting assertion for the associated hypersurface stack.