  We show that the recently reported anomalies in $b\to s\mu^+\mu^-$
transitions, as well as the long-standing $g_\mu-2$ discrepancy, can be
addressed simultaneously by a new massive abelian gauge boson with loop-induced
coupling to muons. Such a scenario typically leads to a stable dark matter
candidate with a thermal relic density close to the observed value. Dark matter
in our model couples dominantly to leptons, hence signals in direct detection
experiments lie well below the current sensitivity. The LHC, in combination
with indirect detection searches, can test this scenario through distinctive
signatures with muon pairs and missing energy.
