  We study quantum chromodynamics (QCD) on a finite lattice $\Lambda$ in the
Hamiltonian approach. First, we present the field algebra ${\mathfrak
A}_{\Lambda}$ as comprising a gluonic part, with basic building block being the
crossed product $C^*$-algebra $C(G) \otimes_{\alpha} G$, and a fermionic
(CAR-algebra) part generated by the quark fields. By classical arguments,
${\mathfrak A}_{\Lambda}$ has a unique (up to unitary equivalence) irreducible
representation. Next, the algebra ${\mathfrak O}^i_{\Lambda}$ of internal
observables is defined as the algebra of gauge invariant fields, satisfying the
Gauss law. In order to take into account correlations of field degrees of
freedom inside $\Lambda$ with the ``rest of the world'', we have to extend
${\mathfrak O}^i_{\Lambda}$ by tensorizing with the algebra of gauge invariant
operators at infinity. This way we construct the full observable algebra
${\mathfrak O}_{\Lambda} .$ It is proved that its irreducible representations
are labelled by ${\mathbb Z}_3$-valued boundary flux distributions. Then, it is
shown that there exist unitary operators (charge carrying fields), which
intertwine between irreducible sectors leading to a classification of
irreducible representations in terms of the ${\mathbb Z}_3$-valued global
boundary flux. By the global Gauss law, these 3 inequivalent charge
superselection sectors can be labeled in terms of the global colour charge
(triality) carried by quark fields. Finally, ${\mathfrak O}_{\Lambda}$ is
discussed in terms of generators and relations.
