Within a systematic approach based on the dimensionally regularized
nonrelativistic quantum electrodynamics, we derive the complete result for the
two-loop correction to order (α/π)2(Zα)4 for the g factor
of an electron bound in an nS state of a hydrogenlike ion. The results
obtained significantly improve the accuracy of the theoretical predictions for
the hydrogenlike carbon and oxygen ions and influence the value of the electron
mass inferred from g factor measurements.Comment: 11 pages, 1 figur