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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\'₄ₓ (X) and h^2d-1\'₄ₓ (X) of the motive h\'₄ₓ (X).
Ivan Rosas-Soto (Thu,) studied this question.
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