Measurements of the branching fractions of B0 -> K*0 K+ K-, B0 -> K*0 pi+ K-, B0 -> K*0 K+ pi-, and B0 -> K*0 pi+ pi-

Branching fraction measurements of charmless B0→K*0h1+h2− (h1,2=K, π) decays are presented, using a data sample of 383×10^6 Υ(4S)→BBbar 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.