Quantization and groupoid of partially invertible elements of $W^*$-algebra

We present a method of quantization of one-parameter groups of automorphisms of a $G$-principal bundle $\pi:P\to M$ with a fixed connection form $\alpha\in \Gamma^\infty(P)$. This method is based on the morphism of a gauge groupoid $\frac{P\times P}{G}\rightrightarrows M$ into the groupoid $\mathcal{G}(\mathfrak{M})\rightrightarrows\mathcal{L}(\mathfrak{M})$ of partially invertible elements of a $W^*$-algebra $\mathfrak{M}$. We also show that one can consider the Kirillov-Kostant-Souriau geometric quantization as well as coherent state quantization as some particular cases of the proposed approach.