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A general parametrization of the $B^+\to\pi^+ K^0$ and $B_d^0\to\pi^- K^+$decay amplitudes is presented. It relies only on the isospin symmetry of stronginteractions and the phase structure of the Standard Model and involves noapproximations. In particular, this parametrization takes into account bothrescattering and electroweak penguin effects, which limit the theoreticalaccuracy of bounds on $\gamma$ arising from the combined $B^\pm\to\pi^\pm K$,$B_d\to\pi^\mp K^\pm$ branching ratios. Generalized bounds making also use ofthe CP asymmetry in the latter decay are derived, and their sensitivity topossible rescattering and electroweak penguin effects is investigated. It ispointed out that experimental data on $B^\pm\to K^\pm K$ allow us to includerescattering processes in these bounds completely, and an improved theoreticaltreatment of electroweak penguins is presented. It is argued that rescatteringeffects may enhance the combined $B^\pm\to K^\pm K$ branching ratio by a factorof ${\cal O}(10)$ to the $10^{-5}$ level, and that they may be responsible forthe small present central value of the ratio of the combined $B_d\to\pi^\mpK^\pm$ and $B^\pm\to\pi^\pm K$ branching ratios, which has recently beenreported by the CLEO collaboration and, if confirmed, would exclude values of$\gamma$ within a large region around $90^\circ$.Comment: 42 pages, LaTeX, 20 figure

Rescattering and electroweak penguin effects in strategies to constrain and determine the CKM angle