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One can take an Eilenberg-MacLane space $K(A, n)$ for some abelian group $A$, and view it as (locally) constant simplicial sheaf on $Sch/k$, the category of schemes, or smooth schemes, over a field $k$. The model category for motivic homotopy category is the $\mathbb{A}ˆ1$-localisation of the category of simplicial sheaves on $Sch/k$ with respect to the Nisnevich topology.

Is the fibrant replacement of $K(A, n)$ in this model structure a motivic Eilenberg-MacLane space? I.e. does it represent some motivic cohomology group (one without any Tate twists)? This seems a bit unlikely. If not, what is it/what does it represent?

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