Universal suspension via noncommutative motives

In this article we further the study of non-commutative motives. Our mainresult is the construction of a simple model, given in terms of infinitematrices, for the suspension in the triangulated category of non-commutativemotives. As a consequence, this simple model holds in all the classicalinvariants such as Hochschild homology, cyclic homology and its variants(periodic, negative, ...), algebraic K-theory, topological Hochschild homology,topological cyclic homology, ...