  We present results for transverse single-spin asymmetries in proton-proton
collisions at kinematics relevant for AFTER, a proposed fixed-target experiment
at the Large Hadron Collider. These include predictions for pion, jet, and
direct photon production from analytical formulas already available in the
literature. We also discuss specific measurements that will benefit from the
higher luminosity of AFTER, which could help resolve an almost 40-year puzzle
of what causes transverse single-spin asymmetries in proton-proton collisions.
