OS X and umlauts in file names

I'm on an English OS X 10.6.2 and I created a sample file with umlauts in
its name (Überlänge.txt). When I try to stage the file in the terminal, I
can't complete the file name by typing the Ü and hitting the tab key, but I
can complete it by typing an U and hitting the tab key. Unfortunately, after
executing

 git stage Überlänge.txt

I invoked

 git status

and it still shows the file as new file. Should I set some environment
variable to be able to work with files containing umlauts in the name?

Thanks in advance,
Tom