  We report on properties of an optical microcavity based on (Cd,Zn,Mg)Te
layers and embedding (Cd,Zn)Te quantum wells. The key point of the structure
design is the lattice matching of the whole structure to MgTe, which eliminates
the internal strain and allows one to embed an arbitrary number of unstrained
quantum wells in the microcavity. We evidence the strong light-matter coupling
regime already for the structure containing a single quantum well. Embedding
four unstrained quantum wells results in further enhancement of the
exciton-photon coupling and the polariton lasing in the strong coupling regime.
