  To every Fell bundle $\mathscr C$ over a locally compact group ${\sf G}$ one
associates a Banach $^*$-algebra $L^1({\sf G}\,\vert\,\mathscr C)$. We prove
that it is symmetric whenever ${\sf G}$ with the discrete topology is rigidly
symmetric. This generalizes the known case of a global action without a twist.
There is also a weighted version as well as a treatment of some classes of
associated integral kernels. We also deal with the case of Fell bundles over
discrete groupoids. We formulate a generalization of rigid symmetry in this
case and show its equivalence with an a priori stronger concept. We also study
the symmetry of transformation groupoids and some permanence properties.
