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We have computed the branching ratios of the exclusive pseudoscalar (vector)+ tensor modes that are allowed in the decays of the B_c meson. The dominantspectator and annihilation contributions in those decays are evaluated usingthe factorization hypothesis. We find that some of these decay channels, suchas B_c --> (\rho^-, D_s^{*-}, D_s^{-})\chi_{c2} and B_c^ -->\pi^-\bar{B_{s2}^{*0}}, have branching ratios of the order of 10^{-4}, which seemsto be at the reach of forthcoming experiments at the LHC. The inclusivebranching fraction of the two-body B_c decays involving tensor particles isapproximately 1.28 x10^{-3}. At the dynamical level, it is interesting toobserve that the exclusive decays B_c --> K^-(\pi^-)\bar{D_2^{*0}}, \pi^0D_2^{*-}, \eta^{'} D_{s2}^{*-} are dominated by the annihilation contributions.Comment: 14 pages, accepted for publication in JP

Non-leptonic decays of the Bc into tensor mesons