We perform an amplitude analysis of B-+/-->phi(1020)K-*(892)(+/-) decay with a sample of about 384x10(6) B (B) over bar pairs recorded with the BABAR detector. Overall, twelve parameters are measured, including the fractions of longitudinal f(L) and parity-odd transverse f(perpendicular to) amplitudes, branching fraction, strong phases, and six parameters sensitive to CP violation. We use the dependence on the K pi invariant mass of the interference between the J(P)=1(-) and 0(+) K pi components to resolve the discrete ambiguity in the determination of the strong and weak phases. Our measurements of f(L)=0.49 +/- 0.05 +/- 0.03, f(perpendicular to)=0.21 +/- 0.05 +/- 0.02, and the strong phases point to the presence of a substantial helicity-plus amplitude from a presently unknown source.
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