Direct CP, Lepton Flavor, and Isospin Asymmetries in the Decays B→K(*)l+l-

We measure branching fractions and integrated rate asymmetries for the rare decays B -> K((*))l(+)l(-), where l(+)l(-) is either e(+)e(-) or mu(+)mu(-), using a sample of 384x10(6) BB events collected with the BABAR detector at the PEP-II e(+)e(-) collider. We find no evidence for direct CP or lepton-flavor asymmetries. However, for dilepton masses below the J/psi resonance, we find evidence for unexpectedly large isospin asymmetries in both B -> Kl(+)l(-) and B -> K(*)l(+)l(-) which differ, respectively, by 3.2 sigma and 2.7 sigma, including systematic uncertainties, from the standard model expectations.