Rigidity conjecture for upper motives of generalized Severi–Brauer varieties

Let $D$ be a central division $F$-algebra, and let $M_{m,D}$ denote its upper motive associated with the generalized Severi–Brauer variety $X(p^m,D)$. Let $K/F$ be a field extension such that $D_K$ remains a division algebra. Rigidity conjecture. The motive $(M_{m,D})_K$ remains indecomposable. This conjecture concerns the persistence of indecomposability of upper motives under field extensions that do not split the underlying division algebra; the source indicates that a particular case can be proved using the main theorem, while the general statement is not resolved there.