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.