I. INTRODUCTION The bound-electron g factor has been the subject of intense experimental and theoretical inves- tigations over the past decade. Recent measurements for low- Z hydrogenlike ions with a spinless nucleus have reached the precision of 10 − 9 [1–3]. Together with the corresponding theoretical studies these experiments have lead to the new value of the electron mass, four times more ac- curate than the previously accepted value (see Ref. [4] and references therein). Experimental investigations of ions with more than one electron are anticipated in the nearest future. In particu- lar, measurements of the g factor of H-like and Li-like calcium and silicon are currently in progress by the Mainz-GSI collaboration [5]. An extension of these studies to high- Z H-like, Li-like, and B-like systems planned in the framework of the HITRAP project [6, 7] will provide a stringent test of the bound-state QED in the strong electric field of thenucleus. Moreover, investigations of the g factor of heavy B-like ions can lead to an independent determination of the fine structure constant [8]. The motivation for studying the g factor of Li-like and B-like ions follows from the higher theoretical accuracy that can be reached for a specifi c difference of the g factor values of H-like and Li-like ions (or H-like and B-like ions) of the same isotope. Various effects on the g factor of H-like ions were investigated during the last two decades: one-loop [9–16] and two- loop [17, 18] QED corrections, recoil corrections [19–21],nuclear polarization effect [22], and nuclear size effect [23]. The theoretical investigations of the g factor of Li-like ions were con- ducted in Refs. [24–27]. Apart from the one-electron contri butions to the g factor of 2 s state, the effects of the interelectronic interaction should be taken into account in three-electron ions. The one-photon exchange correction was evaluated in the framework of QED in Ref. [25]. The higher- order contributions of the interelectronic interaction were calculated by means of the large-scale configuration-interaction Dirac-Fock-Sturm method in Ref . [26]. Still, the uncertainty associated with these contributions amounts to more than half of the total theoretical uncertainty. The ef- fect of the interelectronic interaction on the QED corrections was treated within two approaches. For low- Z ions the perturbation theory to the leading orders in αZ was employed [24, 26]. For middle- Z and high- Z ions more accurate results were obtained by evaluating the one-electron QED corrections in an effective screening potential [27]. Nevertheless, for all values of Z the uncertainty of the screened QED effects contributes signifi cantly to the total uncertainty, and the rigorous evaluation of these effects is in demand. Hyperfine structure of highly charged ions comprises anothe r sensitive tool for probing QED 2