  We construct the compatible system of $l$-adic representations associated to
a regular algebraic cuspidal automorphic representation of $GL_n$ over a CM (or
totally real) field and check local-global compatibility for the $l$-adic
representation away from $l$ and finite number of rational primes above which
the CM field or the automorphic representation ramify. The main innovation is
that we impose no self-duality hypothesis on the automorphic representation.
