  In this paper we study the asymptotic behavior as time goes to infinity of
the solution to a nonlocal diffusion equation with absorption modeled by a
powerlike reaction $-u^p$, $p>1$ and set in $\R^N$. We consider a bounded,
nonnegative initial datum $u_0$ that behaves like a negative power at infinity.
That is, $|x|^\alpha u_0(x)\to A>0$ as $|x|\to\infty$ with $0<\alpha\le N$. We
prove that, in the supercritical case $p>1+2/\alpha$, the solution behaves
asymptotically as that of the heat equation --with diffusivity $\a$ related to
the nonlocal operator-- with the same initial datum.
