Chow Künneth decomposition for étale motives

In the present article we define an integral analogue of Chow-Künneth decomposition for étale motives. By using families of conservative functors we are able to establish a decomposition of the étale motive of commutative group schemes over a base and we relate to an integral étale Chow-Künneth decomposition of abelian varieties. For a projective variety $X$ of dimension $d$ over an algebraically closed field, we construct integral sub-motives $h_{\acute{\text{e}}\text{t}}^1(X)$ and $h_{\acute{\text{e}}\text{t}}^{2d-1}(X)$ of the motive $h_{\acute{\text{e}}\text{t}}(X)$.