  In this paper, we look at the following question. We consider cellular
automata in the hyperbolic plane, (see Margenstern, 2000, 2007 and Margenstern,
Morita, 2001) and we consider the global function defined on all possible
configurations. Is the injectivity of this function undecidable? The problem
was answered positively in the case of the Euclidean plane by Jarkko Kari, in
1994. In the present paper, we show that the answer is also positive for the
hyperbolic plane: the problem is undecidable.
