  An intrinsically defined gauge-invariant discrete model of the
  Yang-Mills equations on a combinatorial analog of $\Bbb{R}^4$ is constructed.
We develop several algebraic structures on the matrix-valued cochains (discrete
forms) that are analogs of objects in differential geometry. We define a
combinatorial
  Hodge star operator based on the use of a double complex construction.
Difference self-dual and anti-self-dual equations will be given. In the last
section we discus the question of generalizing our constructions to the case of
a 4-dimensional combinatorial sphere
