Quasi-morphisms and symplectic quasi-states for convex symplectic manifolds

We use quantum and Floer homology to construct (partial) quasi-morphisms on the universal cover of the group of compactly supported Hamiltonian diffeomorphisms for a certain class of non-closed strongly semi-positive symplectic manifolds $(M,\omega )$. This leads to construction of (partial) symplectic quasi-states on the space of continuous functions on $M$ that are constant near infinity. The work extends the results by Entov and Polterovich, which apply in the closed case.