Abstract: The Grothendieck ring of varieties over k is the "universal additive invariant" of varieties: it is the free abelian group generated by varieties, modulo the relation [X]=[Y]+[X\Y] for any closed immersion of Y in X. This ring is the pi_0 of a spectrum which encodes higher invariants of decompositions of varieties. In this talk we will introduce the machinery of assemblers and describe a method for detecting multiplicatively "interesting" elements in pi_1 of that same spectrum