Given a finite set $k$ and a countable discrete group $G$, a cellular automaton is a continuous map from $k^G$ to itself which is equivariant with respect to the Bernoulli shift. In this lightning talk, I will explore a noncommutative analogue of this concept, where the finite set $k$ is replaced by a finite-dimensional C*-algebra and the Cartesian product $k^G$ is replaced by an infinite tensor product. These objects, known as quantum cellular automata, were introduced by Schumacher and Werner, with a primary focus on the case of integer actions and simple finite dimensional C*-algebras. I will present generalizations of some of their results to more general groups, and discuss some questions that arise in this broader context.
