The nonmesonic weak decay of Λ hypernuclei is studied in a shell model framework. A complete strangeness-changing weak Λ N → NN transition potential, based on one boson exchange, is constructed by including the exchange of the pseudoscalar mesons π , K , η as well as the vector mesons ρ , ω , and K * , whose weak-coupling constants are obtained from soft meson theorems and SU(6) w . General expressions for nucleons in arbitrary shells are obtained. The transition matrix elements include realistic Λ N short-range correlations and NN final state interactions based on the Nijmegen baryon-baryon potential. The decay rates are found to be especially sensitive to the inclusion of the strange mesons K and K * even though the role of kaon exchange is found to be reduced with recent couplings obtained from one-loop corrections to the leading order in chiral perturbation theory. With the weak couplings used in this study the rates remain dominated by the pion-exchange mechanism since the contributions of heavier mesons either cancel each other or are suppressed by form factors and short-range correlations. The total decay rate therefore remains in agreement with present measurements. However, the partial rates which are even more sensitive to the inclusion of heavier mesons cannot be reconciled with the data. The proton asymmetry changes by 50% once heavier mesons are included and agrees with the available data.