  Consider the canonical morphism from the Chow ring of a smooth variety $X$ to
the associated graded ring of the topological filtration on the Grothendieck
ring of $X$. In general, this morphism is not injective. However, Nikita
Karpenko conjectured that these two rings are isomorphic for a generically
twisted flag variety $X$ of a semisimple group $G$. The conjecture was first
disproved by Nobuaki Yagita for $G=\mathop{\mathrm{Spin}}(2n+1)$ with $n=8, 9$.
Later, another counter-example to the conjecture was given by Karpenko and the
first author for $n=10$. In this note, we provide an infinite family of
counter-examples to Karpenko's conjecture for any $2$-power integer $n$ greater
than $4$. This generalizes Yagita's counter-example and its modification due to
Karpenko for $n=8$.
