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An Orlicz space $L^{\Phi}(\Omega)$ is a Banach function space defined byusing a Young function $\Phi$, which generalizes the $L^p$ spaces. We showthat, for a reflexive Orlicz space $L^{\Phi}([0,1])$, a locally compact secondcountable group has Kazhdan's property $(T)$ if and only if it has property$(T_{L^{\Phi}([0,1])})$, which is a generalization of Kazhdan's property $(T)$for linear isometric representations on $L^{\Phi}([0,1])$. We also prove that,for a Banach space $B$ whose modulus of convexity is sufficiently large, if alocally compact second countable group has Kazhdan's property $(T)$, then ithas property $(F_{B})$, which is a fixed point property for affine isometricactions on $B$. Moreover, we see that, for an Orlicz sequence space$\ell^{\Phi\Psi}$ such that the Young function $\Psi$ sufficiently rapidlyincreases near $0$, hyperbolic groups (with Kazhdan's property $(T)$) don'thave property $(F_{\ell^{\Phi\Psi}})$. These results are generalizations of theresults for $L^p$-spaces.

Property $(T_{L^{\Phi}})$ and property $(F_{L^{\Phi}})$ for Orlicz spaces $L^{\Phi}$