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In this paper, we compute the local relative character for 10 stronglytempered spherical varieties in the unramified case. We also study the localmultiplicity for these models. By proving a multiplicity formula, we show thatthe summation of the multiplicities is always equal to 1 over each localtempered Vogan $L$-packet defined on the pure inner forms of the sphericalvarieties. Finally, we formulate the Ichino-Ikeda type conjecture on a relationbetween the period integrals and the central values of certain automorphic$L$-functions for those strongly tempered spherical varieties.

Periods of Automorphic Forms Associated to Strongly Tempered Spherical Varieties