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Let $G,H$ be two countable amenable groups. We introduce the notion of groupcharts, which gives us a tool to embed an arbitrary $H$-subshift into a$G$-subshift. Using an entropy addition formula derived from this formalism weprove that whenever $H$ is finitely presented and admits a subshift of finitetype (SFT) on which $H$ acts freely, then the set of real numbers attained astopological entropies of $H$-SFTs is contained in the set of topologicalentropies of $G$-SFTs modulo an arbitrarily small additive constant for anyfinitely generated group $G$ which admits a translation-like action of $H$. Inparticular, we show that the set of topological entropies of $G$-SFTs on anysuch group which has decidable word problem and admits a translation-likeaction of $\mathbb{Z}^2$ coincides with the set of non-negative uppersemi-computable real numbers. We use this result to give a completecharacterization of the entropies of SFTs in several classes of groups.

On the entropies of subshifts of finite type on countable amenable groups