  Starting from a Hamiltonian description of four dimensional general
relativity in presence of a cosmological constant we perform the program of
canonical quantisation. This is done using complex Ashtekar variables while
keeping the Barbero--Immirzi parameter real. Introducing the SL(2,C) Kodama
state formally solving all first class constraints we propose a spinfoam vertex
amplitude. We construct SL(2,C) boundary spinnetwork functions coloured by
finite dimensional representations of the group, and derive the skein relations
needed to calculate the amplitude. The space of boundary states is shown to
carry a representation of the holonomy flux algebra and can naturally be
equipped with a non-degenerate inner product. It fails to be positive definite,
but cylindrical consistency is perfectly satisfied.
