Symmetry and Inverse Closedness for Some Banach *-Algebras Associated to Discrete Groups

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A discrete group is called rigidly symmetric if for every C*-algebra the projective tensor product ℓ¹()⊗ is a symmetric Banach *-algebra. For such a group we show that the twisted crossed product ℓ¹α,ø(;) is also a symmetric Banach *-algebra, for every twisted action (α,ø) of in a C*-algebra. We extend this property to other types of decay, replacing the ℓ¹-condition. We also make the connection with certain classes of twisted kernels, used in a theory of integral operators involving group 2-cocycles. The algebra of these kernels is studied, both in intrinsic and in represented version.