  We study the interplay of C*-dynamics and K-theory. Notions of chain
recurrence for transformations groups (X,G) and MF actions for non-commutative
C*-dynamical systems (A,G) are translated into K-theoretical language, where
purely algebraic conditions are shown to be necessary and sufficient for a
reduced crossed product to admit norm microstates. We are particularly
interested in actions of free groups on AF algebras, in which case we prove
that a K-theoretic coboundary condition determines whether or not the reduced
crossed product is a Matricial Field (MF) algebra. One upshot is the
equivalence of stable finiteness and being MF for these reduced crossed product
algebras.
