For an odd prime p, we construct integral models over p for Shimura varietieswith parahoric level structure, attached to Shimura data (G,X) of abelian type,such that G splits over a tamely ramified extension of Q_p. The local structureof these integral models is related to certain "local models", which aredefined group theoretically. Under some additional assumptions, we show thatthese integral models satisfy a conjecture of Kottwitz which gives an explicitdescription for the trace of Frobenius action on their sheaf of nearby cycles.
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