The notion of a power structure is closely related to that
of a lambda ring. It is a powerful way to encode operations on certain
generating functions. Gusein-Zade, Luengo, and Melle-Hernandez have
defined a power structure over the Grothendieck ring of varieties. I
will discuss an analog of this on a version of the Grothendieck ring
of pretriangulated categories whose elements represent enhancements
of derived categories of coherent sheaves on varieties.