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Consider the Fano surface of a conic bundle embedded in $\mathbb P^5$. Let$i$ denote the natural involution acting on this surface. In this note weprovide an obstruction to the identity action of the involution on the group ofalgebraically trivial zero cycles modulo rational equivalence on the surface.

Chow groups of conic bundles in $\mathbb P^5$ and the Generalised Bloch's conjecture