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Following Lusztig, we investigate constructible characters, leading coecients and left cells for a nite Coxeter group W in the case of unequal parameters. We obtain explicit results for W of type F4, Bn and I2(m )( m even) which support Lusztig's conjecture that known results about left cells in the equal parameter case should remain valid in the case of unequal parameters.

Constructible characters, leading coefficients and left cells for finite Coxeter groups with unequal parameters