Let $G = \mathop{\rm Sp} (2n, \mathbb C)$ be a complex symplectic group. We introduce a ( $G \times (\mathbb C ^{\times})^{\ell + 1}$ )-variety $\mathfrak N_{\ell}$ , which we call the $\ell$ -exotic nilpotent cone. Then, we realize the Hecke algebra $\mathbb H$ of type $C_{n}^{(1)}$ with three parameters via equivariant algebraic $K$ -theory in terms of the geometry of $\mathfrak N_2$ . This enables us to establish a Deligne-Langlands–type classification of simple $\mathbb H$ -modules under a mild assumption on parameters. As applications, we present a character formula and multiplicity formulas of $\mathbb H$ -modules