Let
F
\mathrm {F}
be a non-Archimedean locally compact field with residual characteristic
p
p
, let
G
\mathrm {G}
be an inner form of
G
L
n
(
F
)
\mathrm {GL}_n(\mathrm {F})
,
n
⩾
1
n\geqslant 1
and let
R
\mathrm {R}
be an algebraically closed field of characteristic different from
p
p
. When
R
\mathrm {R}
has characteristic
ℓ
>
0
\ell >0
, the image of an irreducible smooth
R
\mathrm {R}
-representation
π
\pi
of
G
\mathrm {G}
by the Aubert involution need not be irreducible. We prove that this image (in the Grothendieck group of
G
\mathrm {G}
) contains a unique irreducible term
π
⋆
\pi ^\star
with the same cuspidal support as
π
\pi
. This defines an involution
π
↦
π
⋆
\pi \mapsto \pi ^\star
on the set of isomorphism classes of irreducible
R
\mathrm {R}
-representations of
G
\mathrm {G}
, that coincides with the Zelevinski involution when
R
\mathrm {R}
is the field of complex numbers. The method we use also works for
F
\mathrm {F}
a finite field of characteristic
p
p
, in which case we get a similar result.