The Novikov conjecture and extensions of coarsely embeddable groups

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