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We present a generalization of the black hole solution with sphericalsymmetry already known in the literature for $N$-dimensional $F(R)$ gravitywith a conformally invariant Maxwell field and constant scalar curvature $R$.This solution also includes a generalization of the one corresponding togeneral relativity as a special case. We introduce the formalism for theconstruction of a broad family of spherically symmetric thin shells in $F(R)$theory. We use our generalized solution in order to provide examples of bubblesand thin layers of matter surrounding black holes. We analyze the stability ofthe constructions under perturbations preserving the symmetry, finding thatstable configurations are possible for suitable values of the parameters. Weshow that the extension to higher dimensions does not alter the qualitativebehavior of the thin shells found in four dimensions, with the main differencebeing a change of scale for the different values of $N$.

Black hole solutions and thin shells in N-dimensional F(R) gravity with a conformally invariant Maxwell field