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This article is about Lehn–Lehn–Sorger–van Straten eightfolds $Z$
and their anti-symplectic involution $\iota$
. When $Z$
is birational to the Hilbert scheme of points on a K3 surface, we give an explicit formula for the action of $\iota$
on the Chow group of $0$
-cycles of $Z$
. The formula is in agreement with the Bloch–Beilinson conjectures and has some non-trivial consequences for the Chow ring of the quotient.
