Positive Entropy Actions of Countable Groups Factor onto Bernoulli Shifts

We prove that if a free ergodic action of a countably infinite group has positive Rokhlin entropy (or, less generally, positive sofic entropy) then it factors onto all Bernoulli shifts of lesser or equal entropy. This extends to all countably infinite groups the well-known Sinai factor theorem from classical entropy theory. We also use our methods to deduce spectral properties of positive entropy actions, and we show that the Koopman representation of a completely-positive-entropy action must be isomorphic to the countable direct sum of the left-regular representation.