  We introduce property $(T_{Schur},G,K)$ and prove it for some non-cocompact
lattice in $Sp_4$ in a local field of finite characteristic. We show that
property $(T_{Schur},G,K)$ for a non-cocompact lattice $\Gamma$ in a higher
rank almost simple algebraic group in a local field is an obstacle to proving
the Baum Connes conjecture without coefficient for $\Gamma$ with known methods,
and this is stronger than the well-known fact that $\Gamma$ does not have the
property of rapid decay (property (RD)). It is the first example (as announced
in [Laf10a]) for which all known methods for proving the Baum Connes conjecture
without coefficient fail.
