  Several new transformations for q-binomial coefficients are found, which have
the special feature that the kernel is a polynomial with nonnegative
coefficients. By studying the group-like properties of these positivity
preserving transformations, as well as their connection with the Bailey lemma,
many new summation and transformation formulas for basic hypergeometric series
are found. The new q-binomial transformations are also applied to obtain
multisum Rogers--Ramanujan identities, to find new representations for the
Rogers--Szego polynomials, and to make some progress on Bressoud's generalized
Borwein conjecture. For the original Borwein conjecture we formulate a
refinement based on a new triple sum representations of the Borwein
polynomials.
