  We consider the abelian group $PT$ generated by quasi-equivalence classes of
pretriangulated DG categories with relations coming from semi-orthogonal
decompositions of corresponding triangulated categories. We introduce an
operation of "multiplication" $\bullet$ on the collection of DG categories
which makes this abelian group into a commutative ring. A few applications are
considered: representability of "standard" functors between derived categories
of coherent sheaves on smooth projective varieties and a construction of an
interesting motivic measure.
