Let V be a strongly rational vertex operator algebra, and let \(g_1, g_2, g_3\) be three commuting finitely ordered automorphisms of V such that \(g_1g_2=g_3\) and \(g_i^T=1\) for \(i=1, 2, 3\) and \(T\in \mathbb {N}\) . Suppose \(M^1\) is a \(g_1\) -twisted module. For any \(n, m\in \frac{1}{T}\mathbb {N}\) , we construct an \(A_{g_3, n}(V)\) - \(A_{g_2, m}(V)\) -bimodule \(\mathcal {A}_{g_3, g_2, n, m}(M^1)\) associated to the quadruple \((M^1, g_1, g_2, g_3)\) . Given an \(A_{g_2, m}(V)\) -module U, an admissible \(g_3\) -twisted module \(\mathcal {M}(M^1, U)\) is constructed. For the quadruple (V, 1, g, g) with some finitely ordered \(g\in \text {Aut}(V)\) , \(\mathcal {A}_{g, g, n, m}(V)\) coincides with the \(A_{g, n}(V)\) - \(A_{g, m}(V)\) -bimodules \(A_{g, n, m}(V)\) constructed by Dong and Jiang, and \(\mathcal {M}(V, U)\) is the generalized Verma type admissible g-twisted module generated by U. When \(U=M^2(m)\) is the m-th component of a \(g_2\) -twisted module \(M^2\) for some \(m\in \frac{1}{T}\mathbb {N}\) , we show that the submodule of \(\mathcal {M}(M^1, M^2(m))\) generated by the m-th component satisfies the universal property of the tensor product of \(M^1\) and \(M^2\) . Using this result, we obtain a twisted version of Frenkel-Zhu-Li’s fusion rules theorem.
