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We define Kazhdan-Lusztig bases and study asymptotic forms for affine$q$-Schur algebras following Du and McGerty. We will show that the analogues ofLusztig's conjectures for Hecke algebras with unequal parameters hold foraffine $q$-Schur algebras. We will also show that the affine $q$-Schur algebra$\mathcal{S}_{q,k}^{\vartriangle}(2,2)$ over a field $k$ has finite globaldimension when char $k=0$ and $1+q\neq 0.$

Kazhdan-Lusztig bases and the asymptotic forms for affine $q$-Schur algebras