  We incorporate the effects of redshift space distortions and non-linear bias
in time-sliced perturbation theory (TSPT). This is done via a new method that
allows to map cosmological correlation functions from real to redshift space.
This mapping preserves a transparent infrared (IR) structure of the theory and
provides us with an efficient tool to study non-linear infrared effects
altering the pattern of baryon acoustic oscillations (BAO) in redshift space.
We give an accurate description of the BAO by means of a systematic resummation
of Feynman diagrams guided by well-defined power counting rules. This
establishes IR resummation within TSPT as a robust and complete procedure and
provides a consistent theoretical model for the BAO feature in the statistics
of biased tracers in redshift space.
