  We provide a self-contained introduction to the quantum group approach to
noncommutative geometry as the next-to-classical effective geometry that might
be expected from any successful quantum gravity theory. We focus particularly
on a thorough account of the bicrossproduct model noncommutative spacetimes of
the form [t,x_i]=i \lambda x_i and the correct formulation of predictions for
it including a variable speed of light. We also study global issues in the
Poincar\'e group in the model with the 2D case as illustration. We show that
any off-shell momentum can be boosted to infinite negative energy by a finite
Lorentz transformaton.
