The main result of this note is a hard Lefschetz theorem for the Chow groups
of generalized Kummer varieties. The same argument also proves hard Lefschetz
for Chow groups of Hilbert schemes of abelian surfaces. As a consequence, we
obtain new information about certain pieces of the Chow groups of generalized
Kummer varieties, and Hilbert schemes of abelian surfaces. The proofs are based
on work of Shen-Vial and Fu-Tian-Vial on multiplicative Chow-K\"unneth
decompositions.Comment: 9 pages, to appear in Abh. Math. Semin. Univ. Hambg., comments
welcome