Recoil correction to the bound-electron g factor in H-like atoms to all orders in αZ

The nuclear-recoil correction to the bound-electron g factor in H-like atoms is calculated to first order in m/M and to all orders in αZ . The calculation is performed in the range Z=1-100 . A large contribution of terms of order (αZ)5 and higher is found. Even for hydrogen, the higher-order correction exceeds the (αZ)4 term, while for uranium it is above the leading (αZ)2 correction. As a result, one of the main sources of the theoretical uncertainty for the bound-electron g factor is eliminated