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Final state interactions are considered to formulate the $B$ meson decayamplitude for the $K\pi\pi$ channel. The Faddeev decomposition of theBethe-Salpeter equation is used in order to build a relativistic three-bodymodel within the light-front framework. The S-wave scattering amplitude for the$K\pi$ system is considered in the $1/2$ and $3/2$ isospin channels with theset of inhomogeneous integral equations solved perturbatively. In comparisonwith previous results for the $D$ meson decay in the same channel, one has toconsider the different partonic processes, which build the source amplitudes,and the larger absorption to other decay channels appears, that are importantfeatures to be addressed. As in the $D$ decay case, the convergence of therescattering perturbative series is also achieved with two-loop contributions.

$B^+\to K^-\pi^+\pi^+$: three-body final state interactions and $K\pi$ isospin states