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Let G be a locally compact group,let Ω : G×G→ C*be a 2-cocycle,and let(Φ,Ψ)be a complementary pair of Young functions.In this talk,we consider the twisted convolution(*)coming from Ω over LΦ(G).We present sufficient conditions under which(LΦ(G);(*)),with the maximal operator space structure,becomes a Banach algebra which is completely isomorphic to an operator algebra.We apply our methods to compactly generated group of polynomial growth and demonstrate that our results could be applied to variety of cases.This is a joint work with Serap Oztop and Varvara Shepelska