Chow K\"unneth decomposition for \'etale motives

In the present article we define an integral analogue of Chow-K\"unneth decomposition for \'etale motives. By using families of conservative functors we are able to establish a decomposition of the \'etale motive of commutative group schemes over a base and we relate to an integral \'etale Chow-K\"unneth decomposition of abelian varieties. For a projective variety X of dimension d over an algebraically closed field, we construct integral sub-motives h¹\'et(X) and h²ᵈ⁻¹\'et(X) of the motive h\'et(X).