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V. Voevodsyky laid the groundwork of delooping motivic spaces in order toprovide a new, more computation-friendly, construction of the stable motiviccategory $SH(k)$, G. Garkusha and I. Panin made that project a reality, whilecollaborating with A. Ananievsky, A. Neshitov and A. Druzhinin. In particular,G. Garkusha and I. Panin proved that for an infinite perfect field $k$ and any$k$-smooth scheme $X$ the canonical morphism of motivic spaces $C_*Fr(X)\to\Omega^{\infty}_{\mathbb{P}^1} \Sigma^{\infty}_{\mathbb{P}^1} (X_+)$ isNisnevich-locally a group-completion.  In the present work, a generalisation of that theorem to the case of smoothopen pairs $(X,U),$ where $X$ is a $k$-smooth scheme, $U$ is its open subschemeintersecting each component of $X$ in a nonempty subscheme. We claim that inthis case the motivic space $C_*Fr((X,U))$ is Nisnevich-locally connected, andthe motivic space morphism $C_*Fr((X,U))\to \Omega^{\infty}_{\mathbb{P}^1}\Sigma^{\infty}_{\mathbb{P}^1} (X/U)$ is Nisnevich-locally a weak equivalence.Moreover, we show that if the codimension of $S=X-U$ in each component of $X$is greater than $r \geq 0,$ the simplicial sheaf $C_*Fr((X,U))$ is locally$r$-connected.

A motivic Segal theorem for open pairs of smooth schemes over an infinite perfect field