Change root of a branch in git

I'm using git and want to change the base of an exiting branch. This is caused by a deployment system, which pulls this explicit branch into my production environment. When planning my releases, I create a tag every time I want to go live. But my branch has special changes too, so git reset --hard v1.0 won't work.

Here a small example. I want this

      C---D---E deploy
     /
A---B---F---G master
     \
      v1.0

to become this

                          C---D---E deploy
                         /
A---B---F---G---H---I---J---K master
     \                   \
      v1.0                v1.1

Maybe git rebase is what I am looking for, but the man pages don't help me. Thanks for your replies!