The first examples of such factors were constructed by Popa (2003) using Connes-Stormer Bernoulli shifts of w-rigid groups. In 2005, Ioana, Peterson & Popa obtained other such examples using infinite free products of (amplifications of) w-rigid factors. We will show, extending results of theirs, from finite von Neumann algebras to almost periodic von Neumann algebras, how we can produce new examples of II1 factors with prescribed countable fundamental group. Our proofs rely on Popa’s deformation/rigidity theory.