  We consider the nonlinear and nonlocal problem $$ A_{1/2}u=|u|^{2^\sharp-2}u\
\text{in \Omega, \quad u=0 \text{on} \partial\Omega $$where $A_{1/2}$
represents the square root of the Laplacian in a bounded domain with zero
Dirichlet boundary conditions, $\Omega$ is a bounded smooth domain in $\R^n$,
$n\ge 2$ and $2^{\sharp}=2n/(n-1)$ is the critical trace-Sobolev exponent. We
assume that $\Omega$ is annular-shaped, i.e., there exist $R_2>R_1>0$ constants
such that $\{x\in\R^n\ \text{= s.t.}\ R_1<|x|<R_2\}\subset\Omega$ and
$0\notin\Omega$, and invariant under a group $\Gamma$ of orthogonal
transformations of $\R^n$ without fixed points. We establish the existence of
positive and multiple sign changing solutions in the two following cases: if
$R_1/R_2$ is arbitrary and the minimal $\Gamma$-orbit of $\Omega$ is large
enough, or if $R_1/R_2$ is small enough and $\Gamma$ is arbitrary.
