  Let $G,H$ be two countable amenable groups. We introduce the notion of group
charts, which gives us a tool to embed an arbitrary $H$-subshift into a
$G$-subshift. Using an entropy addition formula derived from this formalism we
prove that whenever $H$ is finitely presented and admits a subshift of finite
type (SFT) on which $H$ acts freely, then the set of real numbers attained as
topological entropies of $H$-SFTs is contained in the set of topological
entropies of $G$-SFTs modulo an arbitrarily small additive constant for any
finitely generated group $G$ which admits a translation-like action of $H$. In
particular, we show that the set of topological entropies of $G$-SFTs on any
such group which has decidable word problem and admits a translation-like
action of $\mathbb{Z}^2$ coincides with the set of non-negative upper
semi-computable real numbers. We use this result to give a complete
characterization of the entropies of SFTs in several classes of groups.
