We report a Dalitz-plot analysis of the charmless hadronic decays of charged B mesons to the final state K-+/-pi(-/+)pi(+/-). Using a sample of (383.2 +/- 4.2) x 10(6) B (B) over bar pairs collected by the BABAR detector, we measure CP-averaged branching fractions and direct CP asymmetries for intermediate resonant and nonresonant contributions. We find evidence for direct CP violation in the decay B-+/- -> rho(0)(770)K-+/-, with a CP-violation parameter A(CP) = (+44 +/- 10 +/- 4(-13)(+5))%.
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