A new construction of factors of type ${\rm III_1}$

We give in this paper a new construction of factors of type ${\rm III_1}$. Under certain assumptions, we can, thanks to a result by Popa, give a complete classification for this family of factors. Although these factors are never full, we can nevertheless, in many cases, compute Connes' $\tau$ invariant. We obtain a new example of an uncountable family of pairwise non-isomorphic factors of type ${\rm III_1}$ with the same $\tau$ invariant.