QED calculations of the nuclear recoil effect on the bound-electron $g$ factor

Fully relativistic approach is applied to evaluation of the nuclear recoil effect on the bound-electron $g$ factor in hydrogenlike ions to first order in the electron-to-nucleus mass ratio $m\mathrm{/}M$ and to all orders in $\alpha Z$. The calculations are performed in the range $1⩽Z⩽20$ for the $g$ factors of $1s$, $2s$, $2p_{1\mathrm{/}2}$, and $2p_{3\mathrm{/}2}$ states. The $\alpha Z$-dependenceofthenontrivialQEDrecoilcontributionasafunctionof$Z$ is studied.