  We prove the Haagerup property (= Gromov's a-T-menability) for finitely
generated groups defined by infinite presentations satisfying the C'(1/6)-small
cancellation condition. We deduce that these groups are coarsely embeddable
into a Hilbert space and that the strong Baum-Connes conjecture holds for them.
The result is a first non-trivial advancement in understanding groups with such
properties among infinitely presented non-amenable direct limits of hyperbolic
groups. The proof uses the structure of a space with walls introduced by Wise.
As the main step we show that C'(1/6)-complexes satisfy the linear separation
property.
