Grothendieck Ring of Pairs of Quasi-Projective Varieties

We define a Grothendieck ring of pairs of complex quasi-projective varieties (consisting of a variety and a subvariety). We describe $$\lambda$$ -structures on this ring and a power structure over it. We show that the conjectual symmetric power of the projective line with several orbifold points described by A. Fonarev is consistent with the symmetric power of this line with the set of distinguished points as a pair of varieties.