Injectivity conjecture I(k;R) for geometric and slice motives

Let $k$ be a field and $R$ a coefficient ring. Write $\operatorname{DM}_{\operatorname{gm}}^{\operatorname{eff}}(k;R)$ for geometric effective motives and $\operatorname{DM}_{\operatorname{sl}}^{\operatorname{eff}}(k;R)$ for slice effective motives, with the former included in the latter. Injectivity conjecture $I(k;R)$. The inclusion

$$\operatorname{DM}_{\operatorname{gm}}^{\operatorname{eff}}(k;R)\hookrightarrow\operatorname{DM}_{\operatorname{sl}}^{\operatorname{eff}}(k;R)$$

induces an injective group homomorphism

$$K_0(\operatorname{DM}_{\operatorname{gm}}^{\operatorname{eff}}(k;R))\longrightarrow K_0(\operatorname{DM}_{\operatorname{sl}}^{\operatorname{eff}}(k;R)).$$

This conjecture asks whether passing from geometric effective motives to the stable category generated by them and their slices creates no additional relations in the Grothendieck group. It is proposed in the context of extending motivic integration to slice motives; the supplied text does not state a resolution.