  In this article we study microwave absorption in superconductors in the
presence of a vortex lattice. We show that in addition to the conventional
absorption mechanism associated with the vortex core motion, there is another
mechanism of microwave absorption, which is caused by the time-dependence of
the quasiparticle density of states outside the vortex cores. This mechanism
exists even in the absence of vortex motion and provides the dominant
contribution to microwave absorption in a broad interval of physical
parameters. At low frequencies, the dissipative part of the microwave
conductivity $\sigma(\omega)$ is proportional to the inelastic relaxation time,
$\tau_{\mathrm{in}}$, which is typically much larger than the elastic
relaxation time, $\tau_{\mathrm{el}}$. At high frequencies $\sigma(\omega)$ is
proportional to the quasiparticle diffusion time across the inter-vortex
distance, $\tau_{\mathrm D}$, which is still larger than $\tau_{\mathrm{el}}$.
