  The nonleptonic two body $B_{u,d,s,c}$ decays involving a light tensor meson
in final states are studied in the perturbative QCD approach based on $k_T$
factorization. The decay modes with a tensor meson emitted, are prohibited in
naive factorization, since the emission diagram with a tensor meson produced
from vacuum is vanished. While contributions from the so-called hard scattering
emission diagrams and annihilation type diagrams are important and calculable
in the perturbative QCD approach.
  The branching rations of most decays are in the range of $10^{-4}$ to
$10^{-8}$, which are bigger by 1 or 2 orders of magnitude than the predictions
given by naive factorization, but consistent with the predictions from QCD
factorization and the recent experimental measurements. We also give the
predictions for the direct $CP$ asymmetries, some of which are large enough for
the future experiments to measure. We also find that, even with a small mixing
angle, the mixing between $f_2$ and $f_2^{\prime}$ can bring remarkable changes
to both branching ratios and the direct $CP$ asymmetries for some decays
involving $f_2^{(\prime)}$ mesons.
  For decays with a vector meson and a tensor meson in final states, we predict
a large percentage of transverse polarization contributions due to the
contributions of the orbital angular momentum of the tensor mesons.
