The Grothendieck ring of stacks
The Grothendieck ring of algebraic stacks was introduced by T. Ekedahl in 2009, following up on work of other authors. It is a generalization of the Grothendieck ring of varieties. For every linear algebraic group G, we may consider the class of its classifying stack BG in this ring. Computing the class of BG is related to the famous rationality problem for fields of G-invariants (Noether's problem). I will give a brief introduction to the Grothendieck ring of stacks, and then talk about some of my results in this area.