  In this paper, we investigate the tensor structure of the category of finite
dimensional weight modules over the Hopf-Ore extensions $kG(\chi^{-1}, a, 0)$
of group algebras $kG$. The tensor product decomposition rules for all
indecomposable weight modules are explicitly given under the assumptions that
$k$ is an algebraically closed field of characteristic zero, and the orders of
$\chi$ and $\chi(a)$ are the same.
