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I can perhaps say something about the first question. $S(H)$ will not be a groupoid under composition since the composition of two projections need not preserve the dot product. However if one first fixes a standard probability space $(X, \mu)$ then one can consider the set of partial isometries $V$ on $L^2(X, \mu)$ such that the range and support are characteristic functions on $X$, i.e., there exists measurable subsets $A, B \subset X$ such that $V^*V(f) = f_{|A}$ and $VV^*(f) = f_{|B}$ for all $f \in L^2(X, \mu)$. This is a groupoid since the range and source projections will always commute.

In this setting it is then natural to define property (T) for measured groupoids. This was first done for probability measure preserving group actions and measured equivalence relations by Zimmer (Amer. J. Math. 103 (1981), no. 5, 937–951).

This definition, as well as analogues of several of the well known characterizations of property (T) for groups (for example the cohomological characterization by Delorme and Guichardet) can be found in the more recent paper of Anantharaman-Delaroche (Ergodic Theory Dynam. Systems 25 (2005), no. 4, 977–1013).

Edit: Actually, I suppose $S(H)$ is a groupoid if you only allow composition when the corresponding subspaces are equal. Rather what I mean is that it is not a pseudogroup, and (at least in the measurable setting) this is the natural thing to use to define representations of groupoids.

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I can perhaps say something about the first question. $S(H)$ will not be a groupoid under composition since the composition of two projections need not preserve the dot product. However if one first fixes a standard probability space $(X, \mu)$ then one can consider the set of partial isometries $V$ on $L^2(X, \mu)$ such that the range and support are characteristic functions on $X$, i.e., there exists measurable subsets $A, B \subset X$ such that $V^*V(f) = f_{|A}$ and $VV^*(f) = f_{|B}$ for all $f \in L^2(X, \mu)$. This is a groupoid since the range and source projections will always commute.

In this setting it is then natural to define property (T) for measured groupoids. This was first done for probability measure preserving group actions and measured equivalence relations by Zimmer (Amer. J. Math. 103 (1981), no. 5, 937–951).

This definition, as well as analogues of several of the well characterizations of property (T) for groups (for example the cohomological characterization by Delorme and Guichardet) can be found in the more recent paper of Anantharaman-Delaroche (Ergodic Theory Dynam. Systems 25 (2005), no. 4, 977–1013).