Geometric retract rationality of norm varieties

Let k be a field of characteristic zero. We show that the norm variety associated to a prime $\mathrm{\ell }$ and an ordered sequence of invertible elements of k is geometrically retract rational. This generalizes a recent result of Balwe-Hogadi-Sawant, where geometric ${\mathbb{A}}^1$-connectedness (an a priori weaker notion) had been proven.