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We deduce one-parameter group properties for pseudo-differential operators$\operatorname{Op} (a)$, where $a$ belongs to the class $\Gamma ^{(\omega_0)}_*$ of certain Gevrey symbols. We use this to show that there arepseudo-differential operators $\operatorname{Op} (a)$ and $\operatorname{Op}(b)$ which are inverses to each others, where $a\in \Gamma ^{(\omega _0)}_*$and $b\in \Gamma ^{(1/\omega _0)}_*$.  We apply these results to deduce lifting property for modulation spaces andconstruct explicit isomorpisms between them. For each weight functions $\omega,\omega _0$ moderated by GRS submultiplicative weights, we prove that theToeplitz operator (or localization operator) $\operatorname{Tp} (\omega _0)$ isan isomorphism from $M^{p,q}_{(\omega )}$ onto $M^{p,q}_{(\omega /\omega _0)}$for every $p,q \in (0,\infty ]$.

Liftings for ultra-modulation spaces, and one-parameter groups of Gevrey type pseudo-differential operators