  We define a generalization of scalar fields with non-canonical kinetic term
which we call exotic k-essence or briefly, exotik. These fields are generated
by the global description of cosmological models with two interactive fluids in
the dark sector and under certain conditions, they correspond to usual
k-essences. The formalism is applied to the cases of constant potential and of
inverse square potential and also we develop the purely exotik version for the
modified holographic Ricci type of dark energy (MHR), where the equations of
state are not constant. With the kinetic function $F=1+mx$ and the inverse
square potential we recover, through the interaction term, the identification
between k-essences and quintessences of exponential potential, already known
for Friedmann-Robertson-Walker and Bianchi type I geometries. Worked examples
are shown that include the self-interacting MHR and also models with crossing
of the phantom divide line (PDL).
