  In this article, we propose a way of seeing the noncommutative tori in the
category of noncommutative motives. As an algebra, the noncommutative torus is
lack the smoothness property required to define a noncomutative motive. Thus,
instead of working with the algebra, we work with the category of holomorphic
bundles. It is known that these are related to the coherent sheaves of an
elliptic curve. We describe the cyclic homology of the category of holomorphic
bundle on a noncommutative torus. We then introduce a notion of (weak)
t-structure in dg categories. By applying the t-structure to a noncommutative
torus, we show that it induces a decomposition of the motivic Galois group of
the Tannakian subcategory generated by the auxiliary elliptic curve.
