  I present one-loop perturbative calculations of matching coefficients between
matrix elements in continuum regulated QCD and lattice QCD with overlap
fermions, with emphasis a recently-proposed variant discretization of the
overlap. These fermions have extended (``fat link'') gauge connections. The
scale for evaluation of the running coupling constant (in the context of the
Lepage-Mackenzie fixing scheme) is also given.
  A variety of results (for additive mass renormalization, local currents, and
some non-penguin four-fermion operators) for naive, Wilson, clover, and overlap
actions are shown.
