  A covariant scheme for matter coupling with a GL(3,R) gauge formulation of
gravity is studied. We revisit a known Yang-Mills type construction, where
quadratical power of cosmological constant have to be considered in consistence
with vacuum Einstein's gravity. Then, matter coupling with gravity is
introduced and some constraints on fields and background appear. Finally we
elucidate that introduction of auxiliary fields decreases the number of these
constraints.
