Suppose $p:\tilde X\rightarrow X$ is the universal cover of $X$. Take $G$ a group where $\pi_1(X,x)$ acts by isomorphisms. I read that if we consider $X\times G$ ($G$ with the discrete topology) and factor out the action of the fundamental group (i.e. consider the orbit space, of the action $\gamma(x,g)=(\gamma x,\gamma g)$, where we act by deck transformations on the first coordinate) we get a bundle of groups. $\alpha:(\tilde X\times G)/ \thicksim \rightarrow X$.
Any reference for this? How is it that group structure on the fibers is defined?
Thanks a lot.