Purity failure conjecture for non-special semisimple groups

Let $k$ be the ground field, let $G$ be a non-special semisimple $k$-group scheme, and let $X$ be a smooth affine $k$-variety. Purity failure conjecture. There exists a smooth affine $k$-variety $X$ such that purity fails for

$$\operatorname{H}^1_{\mathrm{\acute{e}t}}(X,G).$$

The conjecture predicts that every non-special semisimple group admits a smooth affine variety exhibiting failure of purity. The paper has already established such examples for certain groups, notably projective linear groups, but does not specify a general resolution.