Categorification of Chern characters

The Chern character is a central construction with incarnations in algebraic topology, representation
theory and algebraic geometry. It is an important tool to probe $K$-theory, which is notoriously hard
to compute. In my talk, I will explain, what the categorification of the Chern character is and how we
can use it to show that certain classical constructions in algebraic geometry are of non-commutative
origin. The category of motives plays the role of $K$-theory in the categorified picture. The categorification
leads also to the construction of higher invariants such as the secondary Chern characters and secondary
$K$-theory.