We define and study a gluing procedure for Bridgeland stability conditions
in the situation when a triangulated category has a semiorthogonal
decomposition. As an application, we construct stability conditions on
the derived categories of $Z_2$-equivariant sheaves associated with ramified
double coverings of P3. Also, we study the stability space for the derived
category of $Z_2$-equivariant coherent sheaves on a smooth curve $X$, associated
with a degree 2 map $X → Y$ , where $Y$ is another smooth curve.
In the case when the genus of $Y is ≥ 1$ we give a complete description of
the stability space.