  The production of the $K^*(892)$ strange resonance in Pb+Pb collisions at
$\sqrt{s_{NN}}=2.76$ TeV LHC energy is analyzed within the integrated
hydrokinetic model (iHKM) at different equations of state of superdense matter.
The similar analysis is done also for the RHIC top energy $\sqrt{s_{NN}}=200$
GeV for comparison purposes. A modification of experimental
$K^*(892)$-identification is studied for different centralities in view of
possible re-scattering of the decay products at the afterburner stage of the
fireball evolution. We see quite intensive rescattering of the decay products
as well as recombination processes for $K^*(892)$. In addition, the production
of the much longer-long-lived $\phi(1020)$ resonance with hidden strange quark
content is investigated.
