  We perform an amplitude analysis of B+- -> phi(1020) K*(892)+- decay with a
sample of about 384 million BBbar pairs recorded with the BABAR detector.
Overall, twelve parameters are measured, including the fractions of
longitudinal f_L and parity-odd transverse f_perp amplitudes, branching
fraction, strong phases, and six parameters sensitive to CP-violation. We use
the dependence on the Kpi invariant mass of the interference between the JP=1-
and 0+ Kpi 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_perp=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.
