  Due to the work of many authors in the last decades, given an algebraic
orbifold (smooth proper Deligne-Mumford stack with trivial generic stabilizer),
one can construct its orbifold Chow ring and orbifold Grothendieck ring, and
relate them by the orbifold Chern character map, generalizing the fundamental
work of Chen-Ruan on orbifold cohomology. In this paper, we extend this theory
naturally to higher Chow groups and higher algebraic K-theory, mainly following
the work of Jarvis-Kaufmann-Kimura and Edidin-Jarvis-Kimura.
