This note is about hyperkahler fourfolds $X$ admitting a non-symplectic involution $\iota $. The Bloch-Beilinson conjectures predict the way $\iota $ should act on certain pieces of the Chow groups of $X$. The main result of this note is a verification of this prediction for Fano varieties of lines on certain cubic fourfolds. This has some interesting consequences for the Chow ring of the quotient $X/\iota $.
"On Chow groups of some hyperkahler fourfolds with a non-symplectic involution, II." Rocky Mountain J. Math. 48 (6) 1925 - 1950, 2018. https://doi.org/10.1216/RMJ-2018-48-6-1925