  The decay bar B -> bar K* (-> bar K pi) l+ l- offers great opportunities to
explore the physics at and above the electroweak scale by means of an angular
analysis. We investigate the physics potential of the seven CP asymmetries plus
the asymmetry in the rate, working at low dilepton mass using QCD factorization
at next-to leading order (NLO). The b ->s CP asymmetries are doubly
Cabibbo-suppressed \lesssim 1 % in the Standard Model and its extensions where
the CKM matrix is the only source of CP violation. Three CP asymmetries are
T-odd, and can be O(1) in the presence of non-standard CP violation. The T-even
asymmetries can reach O(0.1), limited by the small strong phases in the large
recoil region. We furthermore point out an easy way to measure CP phases from
time-integrated, untagged bar B_d, B_d -> K* (-> K0 pi0) l+ l- and bar B_s,B_s
-> phi (-> K+ K-) l+ l- decays. Analyses of these CP asymmetries can rule out,
or further support the minimal description of CP violation through the CKM
mechanism. Experimental studies are promising for (super) flavor factories and
at hadron colliders.
