In the wiki figure it says "The frame bundle $\mathcal{F}(E)$ of the Möbius strip $E$ is a non-trivial principal $\mathbb {Z} /2\mathbb{Z}$-bundle over the circle."
Shouldn't the frame bundle of the Möbius strip has $GL(1,R)$ as its fiber? Why is the fiber the $\mathbb{Z}_2$ group? What is $\mathbb{Z}/2\mathbb{Z}$ anyway?