  We study Calabi-Yau manifolds which are complete intersections of
hypersurfaces of multidegree $1$ in an $m$-fold product of $n$-dimensional
projective spaces. Using the theory of Coxeter groups, we show that the
birational automorphism group of such a Calabi-Yau manifold $X$ is infinite and
a free product of copies of $\mathbb{Z}$ . Moreover, we give an explicit
description of the boundary of the movable cone
$\overline{\operatorname{Mov}}(X)$. In the end, we consider examples for the
general and non-general case and picture the movable cone and the fundamental
domain for the action of $\operatorname{Bir}(X)$.
