Abstract. In this talk, we study nondiagonal _nite quasi-quantum groups over nite abelian groups. We investigate the Nichols algebras in the twisted Yetter-Drinfeld module category kGkGYD_ with _ a nonabelian 3-cocycle on a _nite abelian group G:A complete clari_cation is obtained for the Nichols algebra B(V ) in case V is a simple twisted Yetter-Drinfeld module of nondiagonal type. This provides a complete classi_cation of _nite-dimensional coradically graded pointed coquasi-Hopf algebras over abelian groups of odd order, and con_rms partially the generation conjecture of pointed _nite tensor categories due to Etingof, Gelaki, Nikshych and Ostrik.

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