Let
G
G
be a finite subgroup of
S
U
(
4
)
\mathrm {SU}(4)
such that its elements have age at most one. In the first part of this paper, we define
K
K
-theoretic stable pair invariants on a crepant resolution of the affine quotient
C
4
/
G
{\mathbb {C}}^4/G
, and conjecture a closed formula for their generating series in terms of the root system of
G
G
. In the second part, we define degree zero Donaldson-Thomas invariants of Calabi-Yau 4-orbifolds, develop a vertex formalism that computes the invariants in the toric case, and conjecture closed formulae for their generating series for the quotient stacks
[
C
4
/
Z
r
]
[{\mathbb {C}}^4/{\mathbb {Z}}_r]
,
[
C
4
/
Z
2
×
Z
2
]
[{\mathbb {C}}^4/{\mathbb {Z}}_2\times {\mathbb {Z}}_2]
. Combining these two parts, we formulate a crepant resolution correspondence which relates the above two theories.