The Novikov conjecture and extensions of coarsely embeddable groups

Let 1 → N → G → G=N → 1 be a short exact sequence of countable discrete groups and let B be any G-C_-algebra. In this paper, we show that the strong Novikov conjecture with coefficients in B holds for such a group G when the normal subgroup N and the quotient group G=N are coarsely embeddable into Hilbert spaces. As a result, the group G satisfies the Novikov conjecture under the same hypothesis on N and G=N.