*Definition of the Grothendieck group and Leftschetz motive.* The Grothendieck group of varieties is a free abelian group generated by classes of algebraic varieties with the following relation:
$$
[X]=[X\smallsetminus Y]+[Y]
$$
for $Y\subset X$ a closed subvariety. Let $\mathbb L$ denote the class of an affine line (the Leftschetz motive).
For the base field $\mathbb C$ the Grothendieck group forms a ring ($[X\times Y]=[X]\times[Y]$).

*Cancelation conjecture.* This conjecture says the Lefschetz motive $\mathbb L$ is not a zero divisor in the Grothendieck ring, i.e., $\mathbb L^{-1}$ exists.

*A counterexample.* Paper [L. Borisov: Class of the affine line is a zero divisor in the Grothendieck ring, arXiv:1412.6194] provides two varieties $X$ and $Y$ (they are Calabi--Yau varieties with the same derived category of coherent sheaves, but they are not birationally equivalent) with the following relation in the Grothendieck ring:
$$
([X]-[Y])(\mathbb L^2-1)(\mathbb L-1)\mathbb L^7=0,
$$
i.e., $\mathbb L$ is a zero divisor (of course, paper shows that all other factors are not zero).

There are papers that use the Cancelation conjecture, say [S. Galkin, E. Shinder: The Fano variety of lines and rationality problem for a cubic hypersurface, arXiv: 1405.5154]. My question is

(1) Is the Cancelation conjecture is important and why?

or, more precise,

(2) Which theorem and theories use the Cancelation conjecture? And which do not?

and also

(3) How does the results of Lev Borisov affect on these theories? Do we need the existence of $\mathbb L^{-1}$ or it is just formal requirement?

Maybe, my questions show my misunderstanding the difference between Motives and the Grothendieck group. I'll be glad if you correct me and help me understand the questions in both cases.