Measurements of the branching fractions of B0→K*0K+K-, B0→K*0π+K-, B0→K*0K+π-, and B0→K*0π+π-

Branching fraction measurements of charmless B0→K*0h1+h2- (h1,2=K, π) decays are presented, using a data sample of 383×106 Υ(4S)→BB̅ decays collected with the BABAR detector at the PEP-II asymmetric-energy B-meson factory at SLAC. The results are B(B0→K*0K+K-)=(27.5±1.3±2.2)×10-6, B(B0→K*0π+K-)=(4.6±1.1±0.8)×10-6, and B(B0→K*0π+π-)=(54.5±2.9±4.3)×10-6. The first errors quoted are statistical and the second are systematic. An upper limit is set for B(B0→K*0K+π-)<2.2×10-6 at 90% confidence level. We also present measurements of CP-violating asymmetries for the observed decays.