  We study pumping of charge in a 2DEG in the quantum Hall regime at filling
factor $\nu = 2$ (2 spin-split levels of the lowest Landau level). For pumping
frequencies that match the Zeeman energy splitting, quantum pumping together
with hyperfine interaction between electrons and nuclei induces transitions
between the spin-split levels. These lead to a step-like change in the pumped
current and to polarization of the nuclei. We present quantitative predictions
for both. Our model provides the first quantitative tool to both control and
measure the amount of local nuclear polarization in a 2DEG.
