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Let $G$ be a group with undecidable domino problem, such as $\mathbb{Z}^2$.We prove that all nontrivial dynamical properties for sofic $G$-subshifts areundecidable, that this is not true for $G$-SFTs, and an undecidability resultfor dynamical properties of $G$-SFTs similar to the Adian-Rabin theorem.Furthermore we prove a Rice-like result for dynamical invariants asserting thatevery computable real-valued invariant for $G$-SFTs that is monotone bydisjoint unions and products is constant.

On a Rice theorem for dynamical properties of SFTs on groups