中文摘要：

设G是一个群.利用Turaev辫子群范畴的性质,在Doi-Hopf数据（H,A,C）上构造一个Turaev辫子G-范畴,其中H,A,C是Hopf代数.进一步,当C为有限维时,在一簇Smash积代数{A#~HC~＊（α）}_（α∈G）上构造一个拟三角Turaev G-余代数A#~HC~＊,其表示范畴与_AM~C（H）是同构的.

英文摘要：

Let Gbe a group,using the properties of Turaev braided group categories,we constructed a Turaev braided G-category over Doi-Hopf datum（H,A,C）,where H,A,C were Hopf algebras.Furthermore,when C was finite-dimensional Hopf algebra,we constructed a quasitriangular Turaev G-coalgebra A#~HC~＊over a family of Smash product algebras{A#~HC~＊（α）}_（α∈G） whose representation category and ~AM_C（H）were isomorphic.