  The existing predictions for the like-sign dimuon charge asymmetry at the
Tevatron are expressed in terms of parameters related to B mesons' mixing and
inclusive production fractions. We show that in the realistic case when
phase-space cuts are applied, the asymmetry depends also on the details of the
production mechanism for the B mesons. In particular, it is sensitive to the
difference in the fragmentation functions of B^0_d and B^0_s mesons. We
estimate these fragmentation effects and find that they shift the theory
prediction for this observable by approximately 10%. We also point out the
approximately 20% sensitivity of the asymmetry depending on which set of values
for the B meson production fractions is used: as measured at the Z pole or at
the Tevatron. The impact of these effects on the extraction of A^s_{SL} from
the D\O measurement is presented.
