KK[i] is the default setting of IsolateNames, which is the head of abbreviations used by Isolate. A KK[i] returned by Isolate is given in HoldForm and can be recovered by ReleaseHold[KK[i]].
KK[i]
IsolateNames
Isolate
HoldForm
ReleaseHold[KK[i]]
Overview, Isolate, IsolateNames.