  We deduce from Sageev's results that whenever a group acts locally
elliptically on a finite dimensional CAT(0) cube complex, then it must fix a
point. As an application, we give an example of a group G such that G does not
have property (T), but G and all its finitely generated subgroups can not act
without a fixed point on a finite dimensional CAT(0) cube complex, answering a
question by Barnhill and Chatterji.
