This is a follow-up of the question: Group completion of Chow varieties.

Let $S$ be a scheme, $M\to S$ a commutative monoid object in algebraic $S$-spaces, ie. an algebraic $S$-space such that, functorially on $S$-schemes $T$, $M(T)$ is a commutative monoid with neutral element.

Each commutative monoid $M(T)$ has its own group completion $M(T)^{\rm gp}$, given by the classical Grothendieck group construction.

Formation of $M(T)^{\rm gp}$ is functorial in $T$, and we may define the fppf sheaf $M^{\rm gp}$ to be the fppf sheafification of $T\mapsto M(T)^{\rm gp}$.

Is $M^{\rm gp}$ an algebraic $S$-space, hence a commutative group object in algebraic $S$-spaces?