  For every smooth quasi-projective surface X we construct a series of
P^{n-1}-functors H_{l,n}: D(X x X^[l]) --> D(X^[n+l]) between the derived
categories of the Hilbert schemes of points for n>max{l,1} using the derived
McKay correspondence. They can be considered as analogues of the Nakajima
operators. The functors also restrict to P^{n-1}-functors on the generalised
Kummer varieties. We also study the induced autoequivalences and obtain, for
example, a universal braid relation in the groups of derived autoequivalences
of Hilbert squares of K3 surfaces and Kummer fourfolds.
