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Given a pair $(M,X)$, where $X$ is a smooth submanifold in a closed smoothmanifold $M$, we study the operation, which takes each operator $D$ on theambient manifold to a certain operator on the submanifold. The latter operatoris called the trace of $D$. More precisely, we study traces of operators,associated with actions of compact Lie groups on $M$. We show that traces ofsuch operators are localized at special submanifolds in $X$ and study thestructure of the traces on these submanifolds.

On traces of operators, associated with actions of compact Lie groups