Abstract
This note is about the Hilbert square $X=S^{[2]}$, where $S$ is a general $K3$ surface of degree 10, and the anti-symplectic birational involution $\iota$ of $X$ constructed by O'Grady. The main result is that the action of $\iota$ on certain pieces of the Chow groups of $X$ is as expected by Bloch's conjecture. Since $X$ is birational to a double EPW sextic $X^\prime$, this has consequences for the Chow ring of the EPW sextic $Y\subset\mathbf{P}^5$ associated to $X^\prime$.
Citation
Robert Laterveer. "On the Chow groups of certain EPW sextics." Kodai Math. J. 42 (1) 170 - 201, March 2019. https://doi.org/10.2996/kmj/1552982512