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A discrete group $\G$ is called rigidly symmetric if the projective tensorproduct between the convolution algebra $\ell^1(\G)$ and any $C^*$-algebra $\A$is symmetric. We show that in each topologically graded $C^*$-algebra over arigidly symmetric group there is a $\ell^1$-type symmetric Banach $^*$-algebra,which is inverse closed in the $C^*$-algebra. This includes new generalclasses, as algebras admitting dual actions and partial crossed products.Results including convolution dominated kernels, inverse closedness withrespect with ideals or weighted versions of the $\ell^1$-decay are included.Various concrete examples are presented.

Symmetry and Spectral Invariance for Topologically Graded C*-Algebras and Partial Action Systems